Where can I play Carcassonne or Colonists of Catan online?
Brettspielwelt hosts Carcassonne and Settlers (as well as a number of other games) which you can play against other people, and Catan.com hosts Settlers, again against other people.

For playing against the computer, or other people, JCloisterZone is a great, free, downloadable clone of Carcassonne.