Nintendo has stated that any games you purchase off of their DSiWare service are only playable on the DSi that they are purchased from. If you ever buy another DSi, or just want to play a DSiWare game on your DSi instead of a friend/sibling/spouse’s system, you won’t be able to do so.
The only instance in which Nintendo will allow a DSiWare game to be transferred is if the system it was purchased on breaks. In that case, gamers must ship both their shiny new DSi and the old, busted one to Nintendo for the transfer.
If you’ve been eyeing a new color scheme, maybe the prospect of having to pay full price and take a hammer/vehicle/rock to your old one to get back old games will change your mind. (Okay, just buying them again might be cheaper.)