There are multiple online games I have found to be comptible with the nintendo DSi system:
•Hullbreach & DSi paint- meant specifically for the DSi, it is good, but the chtrooms and chat/games are the best part of the site
•DSicade.com- good games, but a not so well chatroom system [only one], but still worth visiting
•spaceinvasio.bigpoint.com- not meant for the DSi, but it still works. If you have no other things to do or like space/war related games give this game a try [universe 2 to join expanding P.D.F. alliance [SDK members]
•www.gindis.com-not very good, actually, but its able to spend a little of your time and makes you feel accompished.
•notify me if you find others worth playing