Bagpipes at weddings are great! (not that I’m biased). I understand that some people associate them with funerals, but it’s all in the tunes you play. Not surprisingly, pipers at funerals tend to play the slow and melancholy pieces, to fit the mood. What you want at a wedding are some marches and song tunes.
For the processional, Mairi’s Wedding is a popular one, and so are quick marches like Highland Laddie and Scotland the Brave.
During the signing of the registry, you might want more contemplative pieces, like the Minguly Boat Song, Dark Isle, or the Mist Covered Mountains.
For the recessional, Bonnie Dundee is a nice stately piece. If the bride and groom have a sense of humour, The Battle’s O’er is another good tune for the recessinal.
And then for the entrance of the bride and groom at the reception, there’s always The Clumsy Lover. Nice lively piece that sets the tone for a party.
There’s a message board dedicated solely to piping that you might want to check out for further suggetions: There was a thread a while ago on the topic of Wedding Tunes. For more threads, search for “wedding” in thread titles in the “music” forum.
All of the above tune links are from Bagpipes at Best. It’s a site with a huge number of tunes in MIDI format so you can listen to them with your computer. (Note: since they’re MIDI, not recordings, they’re not completely accurate representations of what the tune will sound like in real life, but good enough to give you an idea of the tune.)