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.
Although I've been out of the game for the past 13 or so years, both MYOB and Quicken / Quickbooks are pretty much the main players.
Just a word of warning though...Generally the software purchase is for a single years version. All the tax updates etc you won't get automatically unless you pay the yearly fee to keep the software up to date.
Having said that, MYOB is popular and certainly easy to use.
