Common situation:
Install went fine. Supplied correct username and password, and user can login successfully.. but when he/she try and go anywhere, (stats, cats, blogs, Options, Templates, users.. ) he/she is forced to login again.

Before start yelling, make sure you go through all this stuff:

1. You MUST use the same base URL as you have set in $baseurl to log in.

2. If it is local installation URL has to start with http://localhost, but not with http://somename. Or you can use 'fully qualified name' if you are in local network for testing.
EG : $baseurl='http://machinename.full.domain.name:8080/b2evolution/blogs/

3. If you had b2evolution installed in another folder before on the same server/domain, it is possible that the login cookies of the other/old installation override the new ones (check the cookies spec to see how funky this can get :P) . You can either delete your old cookies or name this new installation differently so that cookies don't compete any more. Change the $b2evo_name setting in /conf/_advanced.php . You *must* do this if you run multiple b2evo installations on the same domain.

4. At last, make sure you do have set $b2evo_name = 'somename' as a single word without any space. Believe me, it may cause the problem...

If anything goes wrong, make a search on the support forum this topic.
Cheers!

[edited by FP]