Spybot-S&D does support many common browsers.
As for resident protection, Spybot-S&D contains the Resident ‘ TeaTimer’ which is completely browser independent. It is a Spybot-S&D tool perpetually monitoring the processes called/initiated. In addition, TeaTimer detects changes to some critical registry values.
Spybot-S&D supports detection in cookies, history, start & search pages and bookmarks of these browsers (plus cache for Internet Explorer and Opera):
Firefox pre-0.9, 0.9, 1.x, 2.0, 3.x and old Firebird variants
Microsoft Internet Explorer 5.0, 5.5, 6.0, 7.0, 8.0
Netscape Communicator 4.x, 6, 7
Opera 4.x, 5.x, 6.x, 7.x, 8.x, 9.x
Seamonkey 1.0.x, 1.1.x
Thunderbird 1.x, 2.x (where applicable)