In our experience, bigger business accept them, smaller ones often not, and, as of a few years ago when we were in Belize, many charge extra if you use charge cards or traveler's checques. If you know ahead where you're planning to stay, ask ahead; we used a combination of cashier's checks, traveler's checques, VISA card, and cash.
It makes me feel better to have them with me because if I lost everything (including the checques, ATM card, charge card, cash) I could have the TCs replaced; it's worked for others but - gratefully - I've never had the need. I rarely use them in CA unless a Spanish school, dive shop, or lodging option requests them for payment or charges more if I use my VISA card since I don't like to pack around much cash; this happened 3 places on a recent trip to Honduras. What I don't use I just save for another trip, but you can cash them in at the bank when you get home if you'd rather.