In my group, we have sort of agreed to start most of our games at 2nd level. Like already mentioned, there's always the chance to get PC's killed very easily at level 1. There's really a huge difference between 1st and 2nd level, but usually everybody levels up after the first session or the second maximum, so we decided to skip the "compulsory" first session to get to 2nd level. In addition to increased early PC survival rate, 2nd level also gives the chance to make multiclass characters right from the beginning, but doesn't really take much away from building and evolving the characters, which we also enjoy very much.
We still regularly start games at 1st level or at higher level for games with monster races. Many different people DM in my group so the games tend to differ quite a lot from one another.