Phoenix Wright: Ace Attorney is a story based game where you progress through several murder cases. It's over the top writing and style make it mildly fun, but the gameplay i pretty lacking. It's been re-printed several times by Capcom and keeps selling out - I bought it from Amazon.ca last fall. A sequel for it is set to hit sometime this year.
 
Advance Wars: Dual Strike has been the main game I play on the DS. I got it last summer, and have sunk hundreds of hours into it. The graphics are a bit of a werid update from the GBA games, but the new types of units and strategies more than make up for it. If you at all enjoy turn based strategy games, this one is highly recommneded.
 
Otherwisre, I have Brain Age and Mario Kart : DS. Both aren't too bad - Mario Kart is fun online, but the snakers kind of ruin it for me. The online matchmaking seems to work pretty well at matching up people with similar experience and skill levels.
 
I've heard great things about Elite Beat Agents, but it looks pretty cheesey to me.
 
Oh, and to reference the "wireless card" - DS has built in WiFi compatibility, no add-on or accessory is required. 

 Not many games support online functionality, though. But there is no extra hardware required to go online.