For the video of this please visit http://www.youtube.com/watch?v=OhSTUZM6L48

Intro: Welcome to my first video in my new series :Leaguides. This video will focus on quintessences. Why you should and shouldn't select certain quints, which ones provide the most value, and which ones I feel are weakest. There will be some math done here, and a fair amount of what seems like theorycrafting, but I have done both research and playtesting with a lot of what is discussed here. I hope you can learn something today, and pass this onto your friends if you found it helpful. Don't forget to thumbs me up and leave a comment letting me know if you disagree, or anything you feel I left out so I can include it in my next guide.
For reference, all quints discussed here will be tier 3.
I'm going to start out with a quint I have been using recently, and have found it exceptionally useful in my efforts. That is the Quint of Vigor, which provides HP/5 regen. Let's go over some math, and compare it to the Quint of Fortitude which provides flat HP and see which one fares better.

Greater Quint of Fortitude - 26 HP (78)
Greater Quint of Vigor - 2.7 HP/5 (8.1/5)
It takes 48.148-- seconds for the regen quints to provide more hp. This was calculated by seeing how many seconds it took for the HP/5 to provide more overall hp to your champion than the flat hp. More details coming up next.

Let's now take a look at a champions base and per level stats, and compare those to what the quints provide as well.
Jarvan as an example:
Base Stats (Per Level Stats)
HP- 510 (90)
HP/5 - 7.7 (.7)
The HP quints provide about 15%~ of your starting hp, and less than one full level of hp gain.
The HP/5 quints provide about 105%~ of your starting hp/5, and more than 11 levels of hp/5 gain.

There are a few downsides however to using HP/5 quints over flat HP.
-You are a little more susceptible to burst damage, early game especially where the flat hp provide a larger percentage of your total hp.
-You have to take damage for the HP/5 quints to begin to provide more benefit than flat hp.
-And finally, which is somewhat debatable, EVERY TIME you leave your base with full hp, the hp/5 quints need another 50 seconds to provide more overall HP than the flat HP quints. This goes back to the first two downsides. Basically if you go out into a teamfight, and you die in less than 48 seconds after taking damage, you would have been better off in that specific circumstance with flat hp.

All this being said, I find that during the laning phase, and even later in the game you tend to take damage in small exchanges of poke, and tanking creep waves/jungle creeps so as to make the HP/5 more effective. I also feel the numbers speak for themselves. Every other type of sustain has been nerfed recently as of the Nautilus patch. Wriggles, Hextech, HP pots, most types of sustain have been nerfed, including Soraka and Sona in essence. Hp/5 still hasn't been touched really besides Warmogs. Sustain is powerful, ask Riot.

Now WatchMeSC you say, what about per level runes? Well per level runes follow the same rules for the most part. They provide better benefits starting generally at around level 9. However, in low-mid ELO's most games are decided earlier rather than later I have found. So having a larger chance of swinging the game in your favor early is generally a strong thing to consider as an advantage to the Flat runes rather than the per level which is a little less tangible. Also some champs don't fully come into their own until level 9 or later even, and if that is the case there are two options to consider. You can try to play safe using per level runes, and make your peak at level 9 about as strong as it would have been with flat runes. Or you can try to use flat runes to strengthen your normally weak early game. I find that both options are generally viable, it depends on your playstyle more than anything how you choose to approach this choice.

Now let's take a quick look at some more intangible runes that are hard to decide their actual value:

Greater Quint of Swiftness - 1.5% (4.5%) movespeed increase
Greater Quint of Wisdom - 2% (6%) experience increase
Greater Quint of Avarice - 1g/10 (3g/10)
Greater Quint of Vampirism/Transmutation - 2% (6%) Lifesteal/spellvamp

Greater Quint of Swiftness - 1.5% (4.5%) movespeed increase
For Swiftness let's take a look at Jarvan again for consistencies sake
Base Movespeed - 315
Boots 1 Movespeed - 365
Boots 2 Movespeed - 385
Now let's factor in the Movespeed quints
Base Movespeed - 329
Boots 1 Movespeed - 381
Boots 2 Movespeed - 402

The most noticeable increase there is the difference between Boots 2 without movespeed, and Boots 1 with MS Quints. I can't really talk too much about how strong they are, or how cost effective because it depends a lot on the champ you use and your playstyle again. I will say that every single champ in the game can benefit from moving faster though. I think the time when they shine the most is late game, when the majority of other runes fall off signficantly(a little more on this later). Movespeed quints combine extremely well with champs that need to initiate or maintain kiting control over opponents. Also items that add movespeed such as FoN and Trinity Force/Phantom Dancer stack well with movespeed quints. Currently MS quints make the current common opening for some AP mids of Boots + pots even stronger. If you start with MS quints and boots, and your opponent doesn't start with boots the advantage you have in mobility is incredible. Keep in mind movespeed is one of the rarest stats in the game as well. Most of the items that provide movespeed are expensive, or are not really viable item's for most champs.

Greater Quint of Avarice - 1g/10 (3g/10)
The gold quints are relatively easy to calculate. At 3/10 they provide 18 gold per minute. This is 180 gold per ten minutes. So just add that up for every ten minutes your average game goes and you will get their actual value in game. Most of the time its around 500 gold I have found. Basically its about the equivalent of one free last hit per minute. Not too flashy.
Note: Colby from ColbyLoLVideo's on youtube (go check him out!), wants me to make a note that these quints are especially effective and almost necessary on supports. I can see his logic, but I still feel like MS quints would provide a generally better experience for a support.

Greater Quint of Wisdom - 2% (6%) experience increase
Xp quints provide a benefit until level 18 only, is what it seems like. Being at a higher level than your opponent can be not only a psychological advantage, but also an obvious advantage of having your skills leveled up more. I however, do not use them because they literally provide you nothing late game whatsoever.

Greater Quint of Vampirism/Transmutation - 2% (6%) Lifesteal/spellvamp
Now the lifesteal and spellvamp quints provide a benefit similar to other quints that effect your champions HP in some way. The best benefit in my opinion about these quints is that they scale positively with level. Other quints tend to fall off late game or become completely useless. The more damage and AP you buy, the better these quints become. They also naturally gain strength with level for the lifesteal ones, and some masteries and other runes also help the spellvamp ones. These quints are relatively specific on which champs can effectively use them. Just like most runes there is a hidden downside. These quints are not as good early game, but not only because they don't return much in the way of HP. They are generally not as good because they require you to be attacking or casting spells a lot, which first of all will push your lane more than you want in most cases to get the most out of the runes. Also, in the case of the spellvamp quints, you can end up using a lot of mana to get the amount of HP you need returned to make them slot efficient early. However, these are minor gripes, and these runes seem really strong, especially in theory. I haven't personally used them though.

I won't be going over the generic quints here such as Flat AD, Flat AP, Amor and the like. Many of these other quints are able to be easily calculated by doing simple math on the stats they provide compared to starting items. Now that we have done some math, let's try and go over which quints you should be focusing on for general champion use.

Let's do a recap of the runes in each category sold in the store.
Abilities - I find that the Magic Pen runes are underused in this category for one reason or the other. Mostly I find that the AP runes stack better with most champs who would use them because they are inevitably going to get Deathcap, which stacks the AP a little better than the Pen runes. I find that the flat AP runes in this category are far superior to the scaling ones, because it takes so long for them to catch up in this case.

Defense- For this category I find that the Flat MR runes are probably the best bet overall for most champs. Considering the armor bonus is lower, all champs scale up armor with level, and only some scale up in MR. Flat Armor is passable for jungling, but I find HP/5 to be better for many reasons. (Time used traveling from camp to camp, waiting in bushes for ganks, armor scales up with level and you generally buy armor anyway, etc)

Health - I have already talked at length about HP vs Hp/5 so you can make your own decision there. I find that the 4.5% increased health is not a viable option. Using Jarvan as an example again, his max HP at level 18 without items is 2040, and the 4.5% increased health adds up to 91.8 HP at that point. It scales a little better with more HP items as well obviously. However, the scaling HP/level runes seem to provide a larger bonus at that point anyway (145.8). You would need a lot of HP to make the 4.5% increase better.

Mana - I find that for quints, there are almost always better options for casters than to get mana quints, however if you do decide to go that route I will suggest which ones are the most beneficial. I never found the energy regen quints to be that effective personally, because they didn't seem to make a big difference. The rate at which energy regens naturally makes the energy regen runes seem pitiful by comparison. If you are going to pick mana regen, pick the per level ones surely. They nearly match the flat regen ones at level 5, and surpass them at level 6. Totally worth it. I don'd find the max mana to be that great, although it can be very niche-tastic on Ryze in certain cases. Gives him a decent chunk of damage early game. (Credit to FirstChoice for reminding me about that)

Attack - I find the critical chance and critical damage are very niche. Only specific champions can benefit much from them, and if you are use champions it depends on how you build them as to how effective they will be. Attack speed quints are sometimes used for jungling, but I still find HP/5 to be better in general. As for the Flat vs Scaling AD quints, it depends on your playstyle and what champions you tend to use. Some AD carries hit their peak at 9, some are stronger earlier. Base your decision on those factors I would say. Keep in mind that last hitting is easier early game with Flat AD runes, and the damage output is quite nice if they have a decent skill that scales decently off of AD. More damage late game is always welcome as long as you don't lose the early game too hard and make the extra damage from the scaling quints not enough to compensate. Armor pen is again good on specific champs I find. However it scales negatively with levels. As I stated, all champs gain armor with level, and reducing armor by 10 does less and less the more armor they gain.

Utility - Have all been covered at length previously.

Good early game quints - HP/5, MR, Flat AD/Armor Pen, AP
Good late game quints - Movespeed, Lifesteal/Spell Vamp, Scaling Runes