One challenge in starting a new game is getting the group together. To get around that, you can very easily start the group off all together, but that can leave some things feeling a bit off. After all, how did the group come together in the first place?
This question bugged me in several games, so I was really happy when I came across Dresden Files and it had a way to handle it. In Dresden Files - which is an Urban Fantasy genre game where the PCs are expected to work as a group but not as much as in say D&D - as part of character creation you make ties with two other PCs in the game. This is done with stories. You start a story and say how the event began. You then hand it to another player who says how their character progressed the story - for good or ill. It is then handed off to a third player who says how their character resolved the issue - again for good or ill. Everyone does this, and the only rule is no duplicate connections unless there is no other choice.
It works well, but it's not without problems. It's possible to end up with players not connected in a way that is useful to bringing people together. It is also possible that due to a choice being made that two characters won't want to work together. This can be avoided with everyone knowing what the intention is, but I've seen it happen on accident too.
For starting a whole group together I really like how Masks: A new Generation does it. Now, this works best for games where the group is going to be working together closely a lot - like a superhero game, or D&D type games - but I'm sure it could also be modified easily enough for other games.
How it works is this, each player answers a question about something with the event that relates to their character. In Masks what that question is is defined by the archetype the character plays. So the Beacon says how the group found signs it was something bigger, the Bull tells about a powerful enemy the group took down, and the Delinquent talks about what rules - and whose rules - had to be broken to come out on top.
This works well because everyone is injecting things that interest them, or are tied to their character, into this event. With every addition the event itself gets fleshed out. In the end the group has a whole picture of what happened, everyone has done something to tie themselves to it, and there is a common thread linking everyone together.
Both ways work great. So give one a try if you need to bring people together.