This is an update of my first guide, I've been primarily a Malphite player for a while when solo top and jungling, and usually rely on a specific core build with some situational items.

While not all the information will match your playing style, at least the viability of items for situations is something I've tested a lot.

The basis and namesake of this build is focusing on and taking advantage of early mobility to either harass enemy champions to diminish their farming, or allow effective zoning so that you can acquire large amounts of armor late in the game. If you don't like the name, sorry, but when played against the right opponent, his role is simply that of relentlessly poking laning opponents in an unwanted fashion.

Also included is a somewhat overkill jungling guide, but a rune/mastery/item build that allows Malphite to clear jungles and duel with the best early on, and turn that commanding authority into powerful lvl-6 ganks and late game tanking.
The second page lists a more Jungling oriented Mastery/Rune/Item page setup.

This is current as of the Diana Patch

While Malphite is typically very mana dependent early, and often item dependent late to function effectively, the role of off-tank and initiator can't be overlooked by opposing teams if you're building well.

Early game, against characters with poor sustain, you have the ability to harass and/or zone them out of a lane. This will make you mana poor quite often, and even if done well you may not be able to initiate a kill when you reach Lvl 6 consistently.
Against opposing champs with reasonable sustain, it's usually better to occasionally harass and conserve mana, and spend the rest of your focus on last-hitting and using the W Brutal Strikes and E Ground Slam skills to mop up minions.

My preferred location is solo top, but the same build has been viable for me on bottom babysitting squishy champions, and even in middle with an even to favorable matchup.

While Malphite has an impressive ability to roam early in the game when played as a tanky off-support if your laning partner is doing an exceptional job, I've found that this is most valuable when you're successfully harassing one lane opponent out of the lane, and your mid would like assistance or harassment.

Another unique way I prefer to build lane Malphite is to effectively abandon the Seismic Shard ability after level 6. Without much ability power, usually within a team with one or two strong carries the damage output of the Seismic Shard isn't worth quite as much as the included slow effect, and running alongside to do damage with a Sunfire Aegis and/or Ground Slam. During early levels, however, the base damage provided by the Seismic Shard spell can't be overlooked even by high sustain champions, and having that slow/haste available on a reasonable cooldown later can be pivotal when focusing targets on the other team.

The importance of initiations in teamfights cannot be overlooked. Malphite has arguably the best initiation combo in the game (R + W + E - then Q at fleeing squishy opponents); however a missed ult at best should delay your team's participation in a full blown fight, and at worst leads to too much of the opposing team being effective for the opening moments of the fight.

I've played Malphite as a support when needed as a counterpick to an extremely AD heavy team, and babysitter for particularly squishy AD carries at bottom, and while certain support items work well ( Shurelya's Battlesong, Aegis of the Legion, Heart of Gold into Randuin's or Iron Solari Locket), Malphite's real strength of being able to shrug off trades with his passive and zone limited sustain opponents is only effective against certain lane comps, and most critically being poor on gold as a part of being a support severely limits his role as tank later into the game.

These can be somewhat interchangeable, though I consider the Greater Quintessence of Health or Greater Quintessence of Armor and MR/Lvl Greater Glyph of Scaling Magic Resist Glyphs to be critical items. Obviously on a champion like Malphite, flat armor Greater Seal of Armor seals provide effective health as well as a more powerful Ground Slam, and are a given.

Early flat health quints boost Malphite's passive early in games, allowing him to jump in, farm minions and sustain more damage with his passive, then fall back and allow it to reset.
Armor Quints in the jungle provide for a thundering Ground Slam for farming camps early, as well as soaking damage from creep camps - which works very well with the passive.

Marks are another story - to maximize effective damage, and make use of existing runes Greater Mark of Desolation (MRPen) marks work very well, though if you have a set of the secondary Greater Mark of Armor from a support or other build, it can work very well when stacked on armor quints, so long as you don't mind a rune page that provides 30+ armor, a bit of scaling MR/Lvl, and nothing else.

That said, the ridiculous all-armor rune page allows a jungling malphite to take Boots and a pair of pots without losing much sustain, and this allows you to decide after taking red buff whether or not a level 2 gank is worth pursuing, or holding off until later (which generally means a Wraiths >> Red Lizard >> Wolves >> Wraiths >> Standby to gank//Recall)

0/21/9 - Offtank.

Flat Armor Masteries, damage reduction, Veteran's Scars, and Honor Guard are must-have in my opinion, the the mana/mana regen available with a mere 8 points in the utility tree are absolutely worth it with how mana hungry Malphite can be when the opportunity to use multiple Seismic Shards presents itself.

I used to recommend taking Clarity and buying boots early for the exclusive purpose of harassing a laning opponent. This only makes sense against a top lane with limited sustain where their enemy jungle also lacks the ability to crush you: that strategy requires you to harass and zone your laning opponent utterly in order to make the risk of being ganked worthwhile.

Instead, given Malphite's versatility as an anti-carry, when laning taking Flash/ Exhaust allows for both summoner spells to be used in defense AND offensive capacity, and later in teamfights the same can be applied to slowing a high value target, and still having a second slow available as a summoner spell to slow and limit the damage output of tanky DPS or AD carry enemies. If there is some responsibility in the lane - be it taking solo top with Teleport, or facilitate babysitting a squishy carry on bottom with Heal or Clairvoyance (but honestly, Exhaust fills this role best, and there are much better choices of support characters with better innate abilities).

The early focus of this build is mobility. Boots first, with enough health or mana potions to sustain through level 6.

Initial item depends on gold the first time back. Chain Vest or Mercury's Treads are ideal, Cloth Armor or Null-Magic Mantle are good interim items. Against AD heavy teams, or if the mobility of second tier boots sooner becomes valuable, then Ninja Tabi are exceptional, but I qualify the utility of Ninja Tabi, even on a champion like Malphite, that for tanky characters no other source of tenacity really make a ton of sense.

Against an AP champion that is installing the hurt - magic resist and mercury treads are the right direction. Anything else, focus on acquiring armor, as it enhances survival against minions, towers, AD champions, and importantly buffs the damage output of the Ground Slam spell.

First completed items should either be a Sunfire Aegis or Glacial Shroud. Both of these provide considerable armor - the sunfire's added health and passive are very impressive, especially as part of the Ult/Brutal Stike/Ground Slam combo package with that 40 Magic Damage per second piling on.
The Glacial Shroud reduces cooldown time and increases mana in the pool, so if you're remaining in lane, or having success roaming it's worth considering first, while building the Giant's Belt side of the Sunfire Aegis enhances his passive and survivability against both physical and magic damage.
In general, the Frozen Heart provides almost Thornmail amounts of armor, as well as mana, but critically includes cooldown reduction, and a valuable aura. I'll get this unless the Sunfire Aegis would be such a boon for farming that it's worth getting. The two put together provides an impressive amount of armor (over 200 armor, more depending on rune page) and valuable passives, allowing you to focus on building Health, Magic Resist, Aura Items, or if necessary, ludicrous amounts of armor.

As for situational items - I tend to choose between Thornmail, Guardian Angel, Warmog's Armor, Abyssal Mask, and Force of Nature. The passive being the difference among these. All are fundamentally defensive items, and intended as 3rd Tier direct counters to fed carries, or being outright focused down. Decide if you need Health, Health Regen, Magic Resist, Armor, or a critical passive from the GA.
It's rare to need Thornmail, but against a team comp that involves an AD Top lane, AD Jungler, and AD Ranged Carry it can easily be the items that renders you almost immune to their damage; at which point you use your ult and communicate with you team to focus down their AP carry then support.
Building Health is always viable with a tank, especially if you're stacking a Sunfire Aegis on top of a Warmog's Armor. It's easier to farm up the 'Mogs, the two add over 1700 health when stacked up, and both help the passive scale even better.
Magic Resist obviously is a must-have against effective AP damage sources. A Negatron Cloak by itself is handy, and typically a Force of Nature makes sense as it provides the most magic resist per gold and per item slot. It tends to take a while to accumulate the required parts and recipe cost, however movement speed and health regeneration % passive is well worth the recipe cost, and the significant jump in magic resist makes it a wholly worthwhile item for late game.
Lastly, when you just need to come back from the dead to lay down the hate, Guardian Angel does just that, while providing you with even more magic resist and armor. Combining a GA with a Warmog's is a classic tank build, but it's used so often for a reason.

On a team where Malphite is functioning as a pure tank - get the Warmog's Armor after the first completed armor build item, then move onto countering the opposing carry with items.
Against an AP nuke, it's between a Guardian Angel, Banshees Veil, Spirit Visage, or Force of Nature. Against a CC heavy team, the Veil wins. Against sustained AP DPS, Spirit Visage. For movement speed and MR, Force of Nature. And whenever the team has a reason to focus down the angry rock in their midst, the Guardian Angel can provide that much more harassment while your teams deals out damage - but this only makes sense if there is a second tanky character on your side.




'Missing' Items:
I used to religiously build a Randuin's Omen as an early item. I don't anymore, simply because the Ground Strike ability provides a limited slow, and lower CDR often allows a faster Seismic Shard to further slow then and make an escape. The primary advantage is having an early Heart of Gold, but even the lowly, and more affordable Locket of the Iron Solari often has a much more successful damage mitigation tool when initiating. The simple reason is that as Malphite, you dictate when initiate occurs, and mentally including the active ability from the Locket of the Iron Solari as part of the initiation sequence means you'll use that item to its maximum ability, especially since the cooldown of the active is on par with the cooldown of Malphite's Unstoppable Force after building a Frozen Heart
Against attack speed / lifesteal beasts, purchasing Frozen Heart is a solid passive counter, but if shutting them down becomes a priority, Thormail is often a more effective deterrent than requiring an active ability from the Randuin's Omen to slow their attack speed, or simply diminish their raw damage output through the Frozen Heart aura and well-placed Exhausts.
Against range attack speed carries, it's usually worth waiting it out on positioning until you can include them in your R/W/E initiation fracas, then use Q to further diminish their health a viability of escape. While Tanky DPS Melee characters tend to be in the center of the team, the combined R + W + E initiate doesn't do enough to limit their damage output, so instead carries or supports need to be the target of this, even if it means delaying use of his Unstoppable Force

If Gold per 10 seconds is a priority, then a Philosopher's Stone and Kindlegem built into a Shurelya's Battlesong is often the preferred route, especially when stacking with the Heart of Gold, and replacing any thought of a Warmog's Armor with this, and focusing on items that provide armor or magic resist instead of pure health for survival in teamfights. When relying on Gp10 for funds, items like the Aegis of the Legion provides extremely efficient damage mitigation for the cost, and is an extremely helpful aura, especially if you're underfunded for one reason or another in your lane or from the jungle.

I've played Malphite in every role, to include mid and bot lane support, and I feel he solidly fits in as a counterpick to AD heavy teams or teams with particularly squishy back lines, and his toolkit can be augmented with item and summoner spell selections as long as you have in mind what you intend to focus on most.

While utility can still be limited in the top lane by aggressive magic damage characters, and jungling can be severely hampered by effective early counterjungling or opposing side early ganks going well, critically Malphite excels because building defensive items and Gold per 10 based support items, and this doesn't diminish his teamfighting utility in mid to late game.