Well, for comparison purposes for those unsure of if they'll need an SD card or not:
I purchased a Wii on launch day. Right now, my Wii's memory consists of:
Game Data (Wii and Virtual Console): 32 files
WiiWare/Channel Data: 3 files
WiiWare and special Wii channels: 3
Virtual Console Channels: 14
Photos Saved to Wii: 0
Blocks Remaning: 1149
The Virtual Console channels eat up most of this memory (although the Elebits save file is particularly huge). If you don't download a lot of them, you should be good. I just recently deleted all my photos to see how much space they were taking, and it's such a minor amount per each file that it isn't even worth mentioning. Screenshots will be no issue for anyone. If one chooses not to purchase an SD card, they'll be fine as long as they don't save like hundreds of custom stages and replays.
Donkey Kong Country (data and actual download) take up a total of 63 blocks, so I would doubt anything would amount to that much as far as custom content goes. In fact, I imagine most of it would be a third of DKC's size or less.
But, I am one of those people who will have a massive amount of custom stages to keep the game fresh. I intend to save most of my fights as well to look back on how to improve. That being said, a 1 or 2 gig SD card would still be a great thing to have simply because you'll more than likely never have to delete anything at all.