Even with management companies handling the units, they are more lkely to be a bit more relaxed with bad credit issues as long as you can show decent income and willingness to pay the required deposits and rents without negotiating.
If you are currently renting, your history with that landlord could be a great asset (or liability) in your being qualified for a new rental. If you've got a good rental history, good income or other favorable background check items, make sure to use these to your advantage when applying for a rental.
As Georgina and Noel mentioned below, a lot of owners and management companies have become more flexible with what they will accept with regards to bad credit.
Best of Luck!