cozy.co is very popular. Keeps a running tab on what tenants owe you, can run background and credit checks, and most of all let's your tenants pay electronically for free.
Rent Manager is web based and has great mobile apps for tenant management and service issues. There are monthly fees, though, so it may or may not be worth it to you depending on how many units you have.
Tenantcloud is nice. I use it with success. I accept payments outside of Tenantcloud, through QuickBooks, but use TenantCloud for everything else, and it has been well. It's continuously being developed, which sometimes is a bad thing, because they break things, but all in all, it's a good tool.
I have also heard a few references to Buildium but haven't used it personally.
App for managing how many units?
What are the features that are must haves?