I'd say the top accounting systems today are Xero and QuickBooks Online. Some people use Wave Accounting because it's free but it may not be enough depending on your needs. QuickBooks Online is the most popular system used in North America and has the most support in terms of accountants certified. There's also a plugin that perfectly integrates Airbnb with QuickBooks Online for automatic importing of reservation income called BNBTALLY (you can find it in the QuickBooks app store) - this makes reservation reconciliation so much easier and precise.
While Quicken has been around for some time, it hasn't seemed to have kept up with the others mentioned. At the same time, some people also use spreadsheets to track everything but if you have more than one listing, it's much better to have a well-supported system. There are a few other options, like Zoho and Sage but there are not as many accountants that support them.
Cheers!