Kate, If you've outgrown QuickBooks and are at least about 30 employees, Intacct has been named "Best to Replace QuickBooks" by Inc. Magazine and is endorsed by AICPA. It also got a five-star review from CPA Practice Advisor, and has been awarded a Software & Information Industry Association finalist two of the last four years. See more here: http://synergybusiness.com/cloud-computing-services-solutions/cloud-computing-services-solutions.php
Do your homework, as ascertaining the best for you is more than just seeing who has endorsements.
Depending on whether you're looking for a personal or business accounting solution, there are a number of online accounting solutions to choose from.