I had the exact same problem with my Sandisk 32gb class 10 card in my 60D...the SECOND time I used it.
When I got my 60D, I bought the Sandisk card indicated above and in all my excitement, forgot to FORMAT it once I put it in the camera! (I guess that makes me Dirty Harry). I also forgot to buy an SDHC reader, so went to Walmart and bought a cheapo. It worked fine. So then, when I put it back in the camera, I formatted it. Took some pix, used the same reader, and my Windows XP computer with all the updates on it didn't even recognize that anything was even plugged in! So I resorted to putting the card back in the camera (where I could see all the pix) and used the "cable connection" to get all the pictures on my computer.
I then ordered a SANDISK brand SDHC reader at Amazon.com. Put my card into it (I didn't format it after putting it back into the camera) and plugged it into my USB port. Worked perfectly! So I bought another SANDISK reader, just in case I lose the first one!
I would think one reader brand is no different than another, but who knows? I figured with Sandisk' reputation of "works first time, every time, all the time" (my absolute requirement!) in my experience with 8-10 CF cards in past years, getting the Sandisk reader couldn't fail. And, of course, it worked perfectly!
Now I format the cards when I put them back into the computer (when I remember..getting old sucks!), pop them into the reader when I want to transfer the pix to my computer, and everything works fine!