Does the USPS accept books wrapped (securely) in the brown paper bags you get in the grocery store? I've got a few hardbacks that I need to send out to members. I'd hate to get to the post office only to be told that they don't accept these kind of wrappings.

Yes, the PO will accept packages wrapped in brown paper and packing tape. 

No string and no boxes originally containing items not allowed in the mail (such as liquor boxes).  Use lots of packing tape tho, some brown paper is actually more brittle than printer paper.  I received one just a few days ago taped firmly across the back, but the brown paper on the top was all ripped and tearing at the edges.  AND no recyling of priority mail packaging for other mail rates.

Yes, LOTS of good sturdy packing tape is crucial!! 

Yes, but it tears easily, so use lots of tape to mummify the package.

Hardcovers are better sent in bubble mailers or small boxes, in my opinion, but you always have the option to mail in whatever wrappings you want.

read this thread, it has some really good tips: http://www.paperbackswap.com/Tips-Making-Paper-Mailers-Work/topic/224782/

If the grocery store bags have anything printed on them the ink will transfer to the book so make sure the book is protected in plastic or something first.