i recomend Bing toolbar for IE. (i usually hate toolbars, but this i use)
not sure if there is similar stuff for FF

then you can enter your mail accounts in it…
it wil notify you when there are new mail… and it is a one click to log in

http://onlinehelp.microsoft.com/en-us/bing/gg316397.aspx

http://www.pcworld.com/article/220032/bings_new_toolbar_is_cool_little_creepy.html
http://www.pcmag.com/article2/0,2817,2380582,00.asp