If you are working on Sharepoint and your sharepoint sites always asks for credentials in Firefox then there are two workarounds which you can do.There can be others but the below mentioned two workarounds are most efficient.
1.Using IE Tabs plugin in Mozilla Firefox
You can download IE Tabs plugin from here https://addons.mozilla.org/en-US/firefox/addon/1419
This plugin will simulate the behaviour of Internet Explorer Tabs inside Mozilla Firefox.And if your sharepoint site is correctly configured to run in IE then after opening it with IE Tab it will work fine in Mozilla Firefox also.
2.Change the network.automatic-ntlm-auth.trusted-uris entry in the about:config in Firefox
Just go to the address bar in firefox and type about:config.Now a configuration file will be opened for you, now here search for the entry named as "network.automatic-ntlm-auth.trusted-uris"
Double click this entry and enter the name of your webserver or the server for which you want firefox to inherit the ntlm credentials.
If you are working locally and have configured your Sharepoint Server also locally then generally adding localhost,Your computer name will do.You can enter comma separated lists for all the sites for which you want firefox to inherit automatic NTLM credentials.
After this step just press ok and refresh your page you will find that now your sharepoint sites can run equally well in firefox also.
If you are facing the same problems in IE 7 then you can read this article to fix the problems