What is the song heard during wedding in South Park episode Royal Pudding?

The song you're thinking of is "Here Comes the Bride" by Richard Wagner. It's a traditional wedding march, and it's played during the wedding of Princess Kenny and Princess Cartman in the South Park episode "Royal Pudding".

The episode cleverly subverts the traditional wedding scene by playing this classic march while showing the absurdity of the situation, as the "wedding" is actually a sham intended to lure the princesses into a trap.