I just discovered that a great many devices that claim to support only SDHC (Secure Digital High Capacity) memory cards will actually also support SDXC (SD Extended Capacity, 64GB and larger) cards. So why do they claim otherwise? Because SDXC cards come formatted with Microsoft's proprietary exFAT filesystem. So, it's sometimes possible to use them anyway, if you first format them with a filesystem that the device understands.
For Android devices - where this problem is most noticeable - there are a few options. FAT32 is the most obvious. Windows won't create FAT32 partitions that are larger than 32GB, but the filesystem itself does support it. There are apparently utilities that will do what you need - I'm not a full-time Windows user, so I'm not sure about them. Under Linux or another Unix, good old mkdosfs will do it. Also, since Android is Linux under the hood, you can format the card with ext4. Of course, you can't use an ext4-formatted SD card under Windows without some jiggery-pokery, but it's a lot saner under Linux. Yay tradeoffs. But, for all this - why the electric, exploding fuck does exFAT even exist?
FAT is a godawful filesystem. It completely sucks. It was designed with the limits of 8-bit CPUs in mind, and was quick-and-dirty, even at that. There have been some features hastily gummed on with staples and tape throughout the years, and FAT32 can even deal with something approaching modern storage capacities, but really, the only reason it still persists is compatibility. It's simple and free of both patent and copyright encumbrance, so everyone and their kid sister can make devices that support it. It's everywhere, therefore it's everywhere. Such is how quasi-standards come to be.
exFAT, however, is none of these things. It's heavyweight, albeit perhaps slightly lighter than NTFS, and patent protection is pending. In practice that means that nobody can implement an exFAT driver without Microsoft's blessing. And they, naturally, won't give such blessing to the developers of Android, or anything else that would compete with their desktop near-monopoly. Apparently they have graciously allowed TV and set-top box manufacturers to license it, but support is very limited outside of Windows (Vista and later, support is strange on XP, requiring specific patches) and Mac OS X (10.6 and later). What's more, there are multiple mutually-incompatible extensions to it, which serve to make it even more heavyweight than it already is - rendering its advantages over NTFS or ext4 completely moot.
So please, just don't friggin' use it. The last thing we need is yet another pseudo-standard that sucks, and moreover, is inextricably attached to the gunky, stinking morass of Microsoft vendor lock-in.