As a DM, I try to give the players some kind of overview that will let them know what kind of world in which they're going to be adventuring. I then let them know what books they can use and what kind of HRs I'm most likely going to use. I also tell them to talk to me about their PC concepts, and before I'll accept a PC, that I want some kind of written background. For some games, I have to do more- for a RIFTS campaign with several players who weren't familiar with the game, I actually went through the books and made a typwritten list of the OCCs (classes) and RCCs (races) that would be permitted in the game, along with a blurb as to what they were and where they could be found. Sometimes the blurb does it all- a superheroic game set in the world of Jules Verne/HG Wells/Space:1889 and played in HERO was easy- everyone showed up with truly solid PCs, complete with visuals, histories, etc.- probably the best campaign I ever ran...
As a player, I try to get as much game-world info as I can, and try to envision what kind of PC would be best for me to play in such a campaign. Sometimes I design a PC particular to that campaign, but most often, I pull a concept from my files and customize it to fit that world. I'm not talking about recycling characters- I just have a file of about 100 or so PC concepts that range from a 2 paragraph outline to fully statted. Some concepts are statted out in multiple RPG systems. I have a PC, Slapstick, who is an insane mercenary who wears clown makeup- he's statted out for HERO, GURPS, RIFTS/Ninjas & Superspies/Heroes Unlimited/Beyond the Supernatural, D20 Modern, Torg, Ace (unpublished), and a few others.
However, I realize its not all about me, so I also try to find out what kind of PCs my fellow players are running. Occasionally, I've even done PCs that had prior relationships with other PCs- brother/brother, brother/sister, sister/sister, employer/employee, or even romantic rivals competing for the affection of some NPC.
On occasion, I get asked to play a particular concept (like a variation on Morley Dotes) or class (usually Cleric or Thief archetypes). I'm cool with that.