IBM / Lenovo are excellent IMO. 😀

Get one that's compatible with Windows XP "F6" if possible, though it's not too hard to slipstream support for additional USB floppies into an XP install disc. 😀
http://support.microsoft.com/kb/916196/en-us

The one I have is an IBM branded unit. It's reliable. The previous one I owned was from Mac Alley, and it broke very quickly.

All I did was take an old laptop of mine running Windows 98 SE and hooked up an ethernet cable directly from it to my modern Windows 8.1 system. After fiddling with some settings I was able to get them talking and I can now pull files off of my 3 1/2" disks by routing it through my old laptop. :B

Considering I haven't heard good things about the quality of the USB floppy drives out there, this might be a more prudent way to go about doing this...

I use a Dell Latitude D series floppy drive... it slides into most of these laptops and it also has a USB port on the side.. since I have a bunch of these laptops, it's best of both worlds for me... works great!

Thank for all your answers! I got an IBM branded one, built in 2006, manufactured for Lenovo.
According to the seller it's basically new and it really looks unused.
And it does read both 1.44MB and 720k floppies.

@Stiletto: Seems I was lucky, it is indeed the USB\VID_057B&PID_0000 Y-E Data model. (Don't think that's very important for me, but good to know.)
@Gemini: I have an old laptop which would be suitable, but I want something simple that doesn't clutter the livingroom with cables. If I ever find a floppy the drive can't read and which is really important to me I will surely use an old internal floppy drive.
@TheMAN: I thought about getting such a drive since I have a Latitude D600, but I don't use that notebook for current stuff anymore since it's running XP and I don't really want to install 7 on it. (It would probably run OK since the RAM is maxed out at 2GB, but the harddisk is not that big and bigger IDE notebook drives cost too much to justify.) And I normally have a second hard disk in the D-bay. Nice point about the D-bay/USB dual use, though.