Birthdays here are usually not really celebrated with songs, but if someone hosts sort of a 'party', I can imagine there is some music in the background. Nothing specific though, generally speaking (of course there's always people doing it differently)
About a wedding, I don't really know, never been to a wedding But I'm guessing it's mostly happy music, or some love songs.
About the mother of all sad events, a funeral, I think it depends on the situation. At my grandma's funeral a little over a year ago, there was no special service inside a church or something, it was all around the grave, and there wasn't really music there. On the other hand, when a cousin of mine got cremated early this year (found out he had cancer at the end of November, died on 1 January, leaving a 10-year old daughter, the world is cruel), I wasn't there (not so close to him) but I heard they played some 'nice' music, like Hotel California.
Which brings me to another question (for everyone): have you guys and girls ever thought about the music you would like to have played at your funeral/cremation/farewell service? I know some people here are like "oh my god I don't even wanna talk about that", which I never understand, because why not simply make sure that your wishes for your farewell service (even if that's 50+ years from now) are written down? You never know what can happen. I once said jokingly that I would like Lordi's "The Devil is a Loser" played at my funeral, although I don't think everyone in my family would appreciate that