I just stumbled across this little recipe to save common searches in gmail. If you turn your search into an URL you can then bookmark it. For example, if you want to search for anything with the label, funny, you would put the following into the search box:
label:funny
Instead just create an URL as follows:
https://mail.google.com/mail/#label/funny
bookmark it and TADA, you now have a saved search!
I haven’t experimented with other types of searches but all keywords could conceivably be prepended with the hash symbol and work similarly.