We had AAA last year for both our car insurance and our homeowner's insurance and as a part of that we had to have a AAA membership. Both of our cars are fairly new, so we haven't had to call for roadside assistance, but my parents, who also have AAA have had to call a few times for their car and they have always responded very quickly and sent someone out within 30 minutes-1 hour (I know that might seem like a long time, but traffic here can be a nightmare).
In terms of the insurance coverage, one of the downfalls for us was that the company providing the actual insurance was not "local." When we had a leak upstairs in a new home we purchased and it broke through the drywall and flooded our downstairs, we called to file a claim, but it was on a Friday night and we got an answering service who assured us that someone would call back. By Monday, we hadn't heard anything, and so I called again and it turned out that the message was never put through. Once I actually did speak with a "real" person, he was great and very helpful and checked up on the progress of things via phone every day (but again, the downfall was that he wasn't there in person to check them out). When we filed an auto insurance claim to get our windshield repaired, it was very easy!
They say that membership has its privileges, and I think that is definitely the case with AAA. In addition to offering roadside assistance, another real benefit of AAA is all of the discounts you get. That alone has probably paid for my membership several times now. You can get discounts on hotels, discounts at restaurants, discounts for admissions to different attractions, and even discounts on eyeglasses and photos! You can search for all of the available discounts online.
For us, it has been money well spent and I would definitely recommend it!
**There are different AAA "Home" offices (when we lived in Utah, the "Main" office for us was out of California, and now there is "AAA Texas") - I don't know if that makes a difference or not, but in both places, we've been pleased.