My AAA card shows me as being a member for over 20 years. So clearly, I think they are "worth it" to me. And FWIW I'm a "value for the money" (i.e. "cheapskate") type person.
Personally, I see AAA as a package of several services, any one of which might not be "worth it" by themselves, but the total package is value for the money IMHO. The most obvious part of that package is the emergency road service. With the 100 mile "gold membership" option, it only takes one major tow (or getting "pulled out of the ditch" in the winter, or...) for the AAA membership to pay for itself. And since both my wife and I commute a fair distance to work, we have actually saved money some years just on the emergency road service (I think one of the more recent times we needed it, was due to one of our "high mileage" cars blowing a coil while driving down the road, thereby making the car useless until it was fixed). IMHO my "emergency kit" (for many years) has always included a (cheap pre-paid) cell phone and my AAA membership card. In most cases, that's all you need...
However, while the emergency road service is nice (and some years that savings alone pays for the membership), they aren't the primary services I use "day to day". What I use more often is maps and travel guides (both high quality IMHO), that you get free with your membership (walk into a AAA office, tell them what you want, show your card, and walk out with it, no cost). Now you can easily buy maps and "guide books" in the stores, but IMHO the AAA versions are often of higher quality. And even if you found maps/guides in the stores that you liked, those costs will still add up over the year (whereas those costs are included in a AAA membership).
And FWIW, I find the travel guides in particular, to be a small "gold mine" when traveling. I've OFTEN gotten lower rates on lodging (sometimes much lower rates) due to AAA only discounts listed in those (free to members) guides. And I also find it very handy when traveling, to have ready access to food/lodging/etc listings (with quality reviews, and often also with contact phone numbers and info on how expensive some place is). It makes it MUCH easier to "comparison shop" when traveling in an unknown area! And it also makes it almost trivial to get a room for the night (often at very competitive rates), with little or no advanced booking/planning. All I do, is go through the listing (for the area) in the guide book, sort by price/features, and then start calling (the contact numbers are included) until I find a (reasonably priced) place with a vacancy. Often this process takes under 5 minutes total, and usually results in a good quality room at a discounted rate!
Which brings up yet another benefit that AAA members have. While it usually isn't advertised much (except in the free AAA travel guide books), there are a LOT of businesses that will give AAA members discounted rates (often 10% or more discount), simply by showing your AAA card and asking for that discount. While the majority of such discounts are from hotels and/or car care places (including some automotive stores), the discounts actually cross the entire spectrum of businesses out there. So you can also think of AAA as a "discount club" of sorts as well!
And finally, while I've never had to use it (thankfully), I feel better knowing that the "bail bond" is also part of my membership. After all, that assured bond, could (if the worst happens) make the difference between you being released (on bond), or spending your time in jail while things get "sorted out". OK, I've never had the need to use it, but I feel more "secure" knowing it is there if I should ever need it.
All things considered, I personally find my AAA membership to be money well spent (but YMMV). And in most years, the discounts (and free maps/guides) alone more than pay for my membership fees. And that doesn't even count the value of the emergency road service, the bail bond service, and the other services that AAA offers (for example, their AAA branded VISA gives me 2%-5% back on all the gas I buy, at just about any gas station I use).
