My wife runs my books and a couple other of her clients on MYOB. I have looked at this with her early on and seems relatively easy to navigate.

I think the other major one is Quick Books which I remember we used with one of my businesses a while back and the accounts people didn't like it much (no idea why).

I agree about server/cloud hosted stuff - no matter how secure the systems are, nothing beats a local instal (with an auto back up system in place) for security in comparison.