Also check this latest post for 11.4 and 12.1: How to get latest Firefox in openSUSE
Update (02-01-2012): As FF is now rapidly releasing new versions, you will get new stable version most of the time from the repos for openSUSE(any version). At the time of writing this update, it have 9.0.1 version available for use.
Update (22-03-2011): Firefox 4 is available in the Mozilla repo now, if you were using the following repo before, please disable or delete it and add the repo in step 1 down there if not added yet.
http://download.opensuse.org/repositories/mozilla:/beta/openSUSE_11.3/ [Remove this repo]
There are some nice new features available and more to come, i hope you guys already heard about it if not read this page. Here i am going to guide you how to install it in openSUSE 11.3 and 11.4. openSUSE has its own repo for it, which updates from time to time upon new packages. So lets start with YaST.
1- Open YaST and click on software repositories, add the following repo.
openSUSE 11.3: http://download.opensuse.org/repositories/mozilla/openSUSE_11.3/
openSUSE 11.4: http://download.opensuse.org/repositories/mozilla/openSUSE_11.4/
Give it a name(any name) and save it. Close software repositories.
2- Now open software management and search for Firefox and select firefox for installation, and there you go.
NOTE: If you have Firefox 3.6.x installed and running, please close it and then open Firefox 4 to start browsing.
Update (18-02-2011): For the users, who have this issue stated below,
Problem: nothing provides libnss3.so(NSS_3.12.9) needed by mozilla-xulrunner20-2.0b11-3.3.i586 Please add this repo, and then try again: http://download.opensuse.org/repositories/mozilla/openSUSE_11.3/ For more details, please read the comments below. Thank You