I have Aflac's short term disability and used it when I had my knee surgery a few years ago. I had no problem with getting them to pay out, and it was really easy dealing with them. There are some different plans with them - I have the one where they pay immediately for accidents (which my knee injury was was) or make me wait two weeks for illness-related disabilities. (The other option was 1 week for illness, but it costs more). I also don't have have it for the full amount of my salary - I decided that if I was home, I would be spending less (no lunches out, not going out to dinner as much, etc.), so that saved $ as well for premiums. Obviously, you'd need to do the math as to how much you can live off, and how long you can wait if it's not an accident.
Another thing to keep in mind with Aflac is that some of their policies give family discounts (not sure if it's just married couples and/or parent/child - or what their policy is on domestic partners), but the short term disability is only an individual plan. So you and your partner would need 2 plans for disability and not be able to share one (if you're able to share their other plans).
I also have their accident policy and cancer plan. Thankfully I haven't had use of the cancer plan, but the accident plan has been used more than I'd like to admit. :)