Somehow this had turned into my highest rated build/guide on Mobafire, so I decided I should expand it a little...
It all started out as a CO-OP game where I stacked 5 Zhonya's hourglasses and a Rabadon's Deathcap on Malphite. It was ridiculously OP. So I played a little more with the idea and here is the affordable result. It uses a combo of armor/MR, health and AP to continue giving him some resistance while utilizing his high AP ratios. AP-tank malph is a lot of fun and can be very powerful.
Pros / Cons
Malphite is a very durable champion
He has good AP ratios and the potential for high damage output
Easy to learn
Relatively cheap IP cost (1350)
Low starting mana
Low movement speed
Not the best farmer
Clairvoyance- Not a bad call, but I don't usually take it.
Cleanse- good choice if you tend to get stun-locked easily, also good if you have trouble escaping, provided you have some other means of escape (ghost, heal, flash).
Heal- Not a bad call if you find you're dying quite a bit, although it's better to change your build to include items that give you more survivability.
Clarity- Malphite has terrible starting mana...'nuff said.
Teleport: allows you to return to your lane faster after recalling or to get up to your allies if you feel like you're too slow.
Exhaust- can be very effective because you can exhaust someone after you ult them so they have trouble getting away. Alternatively you can use it to escape or to help allies escape.
Flash- good in general due to escapability, since you are very slow.
Ghost- You are really SLOW, 'nuff said again.
Ignite- Good for getting that last bit of their health or initiating (especially on champs like Morde, because it drains his shield)
Shurelya's Reverie: this is a pretty good item for Malphite. It's a good escape item because it gives you health and mana regen and a decent (albeit short) speed boost. The solid heath, health/mana regen, and CDR are also really amazing. It's pretty cheap (partially because it builds out of a Philosopher's Stone)and I try to get it early game if I need it.
Chalice of Harmony: A decent early game item because you have NO MANA and the Mana regen allows you to stay in lane longer. Obviously the MR is nice too.
Haunting Guise: A cheap way to get some early game health if you need it, the AP and Magic pen is a nice bonus.
Morello's Evil Tome: Nice AP/CDR item, the 40% CDR (which you'll have with a FH) will make your ult come back ridiculously fast. It also gives some mana regen, which can be helpful since early game you have very little mana.
Void Staff: If the enemy team is stacking a lot of MR this will really piss them off. It will also make you hit anyone's who's not like a 200 pound cat jumping on a marshmallow.
Will of the Ancients: This isn't a very good item for Malph's abilities, but it's a nice support item if you want to play AP/Support/Tank.
Deathfire Grasp: great if there's a super tanky tank (with no MR) on the other team because the active deals a minimum of 30% of their current health. Also gives good AP and CDR.
Soul Shroud: This is another pretty good support item for Malphite...It gives him nice Mana regen and CDR, plus a decent health bonus.
Banshee's Veil: Gives good health, mana, and MR. Also blocks 1 negative spell every 30 seconds.
Force of Nature: This gives you good magic resist and immense health regen. nice choice if you feel like you need to be more tanky.
Sunfire Cape: This will boost your health and armor by quite a bit, and it works well with your ult.
Thornmail: Good choice in general because it has such good armor
Randuin's Omen: Pretty good choice. The active is nice for chasing and helping allies
Warmog's Armor: Not the best choice...you're FAR better off with health items that have more utility.
Zhonya's Hourglass: This will save your butt in a pinch, but don't rely on it to save you when you do something stupid and/or reckless...
Guardian Angel: Think about it
Lich Bane: Great item because it gives you good AP, decent MR, MS, and a proc that works very well with three of your abilities. BOOM (thanks to DuffTime for the suggestion)