Similar conditions apply to DRM-ed material from other suppliers (it probably has to—but don't quote me on that, I am no lawyer—as ownership would imply that you can do what you want with something (within legal bounds))
Some DRM schemas are severely restricted to the devices and
software they run on. For example, MS Reader's
files DRM were toed to MS Reader software that ONLY ran on
So if you are forced to go without a Windows based PC device (e.g. use Linux and Android for your desktop/mobile; and have no money or other reasons not to own Windows), you have lost the ability to read your already-paid-for books
Some DRM schemas lock you into an absolute control from the publisher, to the point of them being able to erase the title from your device.
Practically, the one and only time it was known to happen, Amazon remotely erased the book that they said was published violating author's copyright, illegally. And refunded.
But the risk is that they can do this for ANY of the DRMed ebooks you bought (since such books are restricted to the Kindle software which they control, merely making a backup copy is useless); and done at their whim, and without reimbursement. Yes, this is probably covered in TOS when purchasing the books, but be assured it isn't made painfully obvious to casual reader.
If the ebook is inconvenient to read on your device, you are locked in - can not move it to another device/software that is more to your taste, unless that other device supports the same DRM scheme AND DRM allows copying.
Have a BeOS desktop? You can't read your book there, since there's no Kindle, or MS Reader, or (afaik) Adobe readers for it.
Want to avoid installing buggy and virus-susceptible Adobe PDF reader on your Windows system? You can't read Adobe DRM books on competing PDF readers.
Kindle software runs slow and sluggish as hell on your older smartphone? You can't fire up FBReader, or any other competing ebook reader software that works much better and faster to read your books.
As a note, sometimes "what if a license server or your internet connection is down" is raised as a downside. This might be true for some DRM, but definitely is NOT true for all of them. Amazon's DRM doesn't require an internet connection once the book is bought.