You know what I like? Games that make it easy to get into but then go deep over the long haul. I've mentioned in the past how both Eberron and S. John Ross' Uresia both make it super-easy for D&D people to hop on board. You can create a bog standard surly dwarf or axe-wielding viking for either campaign and then let the GM spoonfeed you the deeper weirdness of the two settings. Similarly, you can play Traveller without knowing much about sci fi other than what you can get out of watching Star Wars, yet there is so much more under the surface.
Low Impact High Weirdness is my new catchphrase for these kinds of games. The big thing about these games is that you don't need a PhD in the setting to whip up a PC, or for the player to know what to do with that PC. There are a lot of rich, wondrous games out there I simply will never play because I don't want to spend umpteen hours conveying the setting to the players so they can make appropriate characters. Most versions of Tékumel, for instance. Or Fading Suns. At its most basic, I don't want to tell players why the setting is cool, I want get them into the game and then show them.
Example: at my Eberron game this last Tuesday the PCs met up with Ms. Johnson in an abandoned tower. Since the party is composed of despicable sky pirates, she brought some back-up. When I described the kobold mercenaries perched on the tower, wearing ewok-style hang-gliders, one of the players nearly jumped out of his seat. This was something new and weird for him. He was startled with the idea of hang-gliding kobolds, pulling quasi-legit merc work in a human city. I loved that reaction.
The player was Jon, who does the same thing to me all the time in his awesome World of Alidor campaign. You can make a regular D&D character for that campaign, and go on regular adventures. Someone with no knowledge of the setting can show up and play cold, but the campaign is chock full of awesome memorable stuff. Hell, after the first session I wrote up a list of things I wanted to do in his campaign, just 'cause it was so loaded with coolness. (Hmm, I've only got three items crossed off that list. Looks like I need to get to work.)
Many games set in the modern world do a good job of being Low Impact High Weirdness. With its easy premise ('occult investigation in the Roaring 20s'), D&D style stats, and percentage skills, Call of Cthulhu is extremely newbie friendly. At least when you don't make the mistake of fetishizing the source material. Most other horror, spy, or action movie games work that way as well. Feng Shui has a boatload of wacky setting info, but actually works better if you only dole it out to the players in bitesized morsels. You start out in a stock action movie and only later see how deep the rabbit hole goes.
Most White Wolf games don't work for me precisely because I need to grok too much at the beginning of a campaign. If the Storyteller has to explain the difference between a Tremere and a Brujah before I can make my PC, then I just don't really want to play. Is that fair, considering that back in the day I had to learn the difference between an elf and a dwarf? Not really. But nowadays I just don't have the time to absorb vast amounts of setting info prior to starting a game. Put me in the game now, and freak me out later.