To expand on the information presented on the interconnectivity between the GameCube and the Game Boy Advance's E-Reader, as pertains to Animal Crossing...
As mentioned above, each card will have a dot-pattern strip and a text code on it. The dot strip will be scannable by the e-reader, at the E-Transfer Machine or ETM. When you scan the card at the ETM, a letter is immediately sent to your mailbox containing a piece of furniture or clothes or something as a present. (How they fit a piano into an envelope, I have no idea. But somehow they do.) The code needs to be written in a letter that you can send to anyone in the town, and you will get a reply from the person on the card instead of the mail's recipient. Again, you'll get a present along with the letter, though usually not the same one you get from using the scanner. Of course, if you get the code wrong, you'll get a very confused reply from the person you sent the code to.
Alright, here's the bit where things get interesting. If you have any intention of trying to find these things out for yourself, please do not read this. (Yes, all three of you.) The text-code printed on the card can land you an NES game. I believe I have gotten all of the regular games mentioned in Ian_Bailey's writeup. How you do this is by sending the letter with the code to the person -on the card-. Then you have a 60% chance of getting an NES game instead of the usual item - this is, of course, affected by various factors that change your character's luck, like making sure the town is weeded, feng shui, and others.
As for the rumored games... I beta-test for Nintendo and one of the save cards I used had the house completely full of NES games, many of which probably require a password or something to unlock them that Nintendo has yet to reveal. Included in the stack was Legend of Zelda, Punchout, Donkey Kong 3, Super Mario Brothers, and others that haven't been mentioned on websites anywhere so I don't have any leeway to inform people they exist. There's some more cool ones though. Since there were rumors of Zelda and Punchout, and especially since reviews of the Japanese version of the game had screenshots of said games... It's released information and I won't get fired for it! Wheeee!
1/23/2003 addendum: I just purchased Animal Crossing. After playing it at work for eight hours a day. I don't know whether this is a compliment to Nintendo or just pitiful.
3/10/2003 addendum: I have learned that some of the NES games are only unlockable via E-Reader cards. This will probably account for the rest of the games.