RPG Systems

In order of personal preference...

Big Eyes, Small Mouth
Short description: BESM is just an all around great RPG system. Simple rules, with more character customization than just about any other system ('cept maybe Call of Cthulhu's percentile system, but CoC's has a much more limited application, and is harder to use), based on the many anime styles out there.
System: Uses 6 sided dice, and nothing else. You'd be surprised just how well this works out. Setting up a character can take awhile, but the high degree of customization is worth it.
Application: Everything... absolutely everything. Medieval fantasy, cyberpunk, mecha, or even non-combat genres like romance and the like... basically, think of it like this... if there is an anime like it, or there could be an anime like it, you can use BESM with it effectively. [The site operator would like to state at this time that Guardians of Order is not paying him in any way (though he'd immediately accept if offered... c'mon guys, get with it... cheap bastards). Thank you.]
How to get the most out of your game: Remember, this is anime based, so comedy is encouraged, the words "be serious' should almost never be heard when playing. Though you can be an existing character, originality is another thing that makes this system great... don't hesitate to make a character completely unlike the norm. Additionally, don't strive for perfection in combat, it takes away from the game as a whole.

Call of Cthulhu
Short description: CoC, the original horror RPG (as far as I know, anyway). The only reason that it's #2 on this page is the fact that a good horror RPG is so hard to make, but CoC does it very nicely. Plenty of info on psychosis, the gods of the mythos, arcane (and more often than not, sanity-breaking) spells is in there, and it's the only RPG to not only heavily discourage combat, but also have the PCs be normal (at the beginning anyway... *insert maniacal laughter here*) humans, easily disturbed and even more easily killed. Anyone who is too used to the D&D way of doing things should look elsewhere.
System: Uses percentile (two 10-sided dice) dice for skill checks, various others for damage. However, due to the percentile system, setting up a character can be a daunting task.
Application: Horror. That's it. CoC doesn't lend itself well to anything else.
How to get the most out of your game: I'm not the most qualified to speak about how to creep out players, so I won't. I can, however, give some tips... This is pretty much the opposite of BESM, comedy is best kept to a minimum, any encounters are meant to be serious and life-threatening, not "Oh, look, another demon. Big deal." Use the character specialization system to it's fullest, and when making characters with other people, be sure to make complimentary characters. An entire party of detectives is not going to get far, doctors, lawyers, or whatever, all have their important roles, the DM should remember this too. If I can find it, I'll post an old InQuest (back before it became InQuest Gamer and thus largely turned to crap) article I had on horror DMing.

World of Darkness (Werewolf)
Short description: Though the World of Darkness universe spans several games (namely, Werewolf: the Apocalypse, Vampire: the Masquarade, Mage: the Ascension, Changling: the Dreaming, Hunter: the Reckoning, and Wraith: the Oblivion [I'm not sure about that last one]), here, I'll focus on Werewolf, largely because it's the only one of the above I've had any amount of experience with, though it should be noted that all of the above systems are cross-compatible (Vampire, Werewolf, and Hunter moreso than the rest). In Werewolf, you play as a (surprise!) werewolf, trying to protect Gaia (the earth-spirit) from the Wyrm (one of three cosmic, all-powerful denziens, I'm not going to explain it here... it has a long, long story behind it all). The other games take different spins on the WoD, and again, I'm not going to explain here.
System: Another nicely simplified system, only 10-sided dice are used. Though it works well, it's not quite as refined as in BESM (well, in my opinion anyway). Setting up a character is easy, with a very good points and skills system in place.
Application: Very limited. Each individual system is tailored to its own storyline, which is both good and bad. Good, in that there is lots of material available to the DM, bad in that to get the most out of it, the purchase of many books is required. Look among all of them and decide which one you like the best. I, myself, want to try Mage eventually. I have no tips for DMs, campaigns are run much like D&D with a different ruleset, except that there is always a greater scheme to things. It's hard to explain without writing pages and pages of background, which I have little inclination to do at this point.
How to get the most out of your game: Taking the above into account, there isn't much more to say... there is plenty of source material available to work with, and it's a good idea to take the books suggestions in high regard. Also, there are a number of handbooks on other shapeshifters to compliment Werewolf, and I highly encourage you to look at them. The only real advice I can give is: players should try their best to stay in character, even moreso than with other RPGs, and DMs should take great care when developing a storyline, though, as with all RPGs, the path shouldn't be entirely pre-written.

AD&D
Short description: Ah, if you're not familiar with this, why are you even here? But for those who started with another system, ignoring this one, it's a simple medieval fantasy setting, though there are a number of sourcebooks to change that. It's changed quite a bit since 1^st edition, but mostly for the better (though I'm not the only one that got a bit thrown by the rules changes from 2^nd to 3^rd). I must confess, I don't know all that much about 3^rd, but when I look into it a bit more, I'll update this. I DO know that 3^rd is easier to get into for beginners than 2^nd was, as well as having a larger weapon list, and more character customization in the form of a refined skill system and feats.
System: Many, many dice are used, be it different types for damage, spell effects, healing, or even monster generation should the DM decide to go that route. It takes a bit to learn, but once you've got it down, it's easy from then on.
Application: As if medieval fantasy wasn't a wide enough genre, the aforementioned sourcebooks can take it into space, fuedal Japan, and others. New uses for the system are easy enough to come up with, it adapts fairly well to other genres.
How to get the most out of your game: First, AD&D is the birthplace of munchkin characters, and there will always be someone who insists on nothing but power, there will also be a rules lawyer, these two often overlap. Do anything you can to discourage this type of behavior, or you will soon regret it. Other than that, read a lot of fantasy. Be it current books, or classics such as Lord of the Rings, these books are home to many good ideas, and may very well inspire you.

More to be added soon.