Officially only supports 32gb. But you can use bigger. I am using a 64gb one without problems at the moment.

Some things I've noted though:

1. Nintendo Support directs you to use a third-party tool for formatting SD cards. However they direct you to do a full format (not necessary and takes forever) and the tool they recommand does an exFAT format for >32gb cards (which won't work with the 3DS) and doesn't even tell you until it's done. Find a different tool, there are several.
2. Before I got my N3DS XL I decided to try transferring my stuff to my 64gb microSD card before I got my N3DS so I could do a quick transfer (if you use a microSD card with your old 3DS, you can just convert the content on the card for use with the N3DS, much faster than an over-the-air transfer). However after moving the files to the new card theme support broke terribly, I lost themes and the theme shop no longer functioned. I don't know if this was an issue with using an unsupported SD card size or what. Going back to the old SD card with the same files worked, and doing an over-the-air transfer to the 64gb card when I got my N3DS worked fine as well.
3. N3DS looks like shows up to 6 digts for blocks free... a 128gb card would likely clock in just under 7 digits, so any bigger could break things? Who knows. Fortunately 128gb is the largest size card available at the moment.
4. I downloaded a ton of VC titles and a dozen or so full games onto my 3DS SD card, and am continuing with my new 3DS. I am only using about 10-12gb. If you are only going to get a few titles 16gb is ample space, 32gb is probably fine for all but the heaviest downloaders (unless you load music onto it or take video with your 3DS, which I don't do).
5. Nintendo warns not to use multiple cards; only use a single card at once. Using multiple active cards at once is not officially supported.