i use mutt with header+body caching, and a small patch to write those cached messages in a maildir format (http://jcs.org/notaweblog/2008/09/29/making_mutt_useful_offl...). this lets me access imap quickly and directly and always have fresh messages, not have to continually run something from cron on my laptop when i'm not reading mail, and still have a full cache of messages to access offline in maildir format if i need it.
on my server i have procmail setup to write a copy of every incoming message (that isn't to a mailing list) to an "allmail" folder that i rotate yearly. this lets me prune my inbox without fear of losing anything, as i occasionally have to search through the allmail folder to find an old email. using mutt's body searching usually finds what i need, and since all of those messages are cached offline, it's relatively quick.
for the rare times when i need to find something that mutt can't find on its own, i use mairix to search the local maildirs, which writes search results to a new maildir, which i can read in mutt.
on my server i have procmail setup to write a copy of every incoming message (that isn't to a mailing list) to an "allmail" folder that i rotate yearly. this lets me prune my inbox without fear of losing anything, as i occasionally have to search through the allmail folder to find an old email. using mutt's body searching usually finds what i need, and since all of those messages are cached offline, it's relatively quick.
for the rare times when i need to find something that mutt can't find on its own, i use mairix to search the local maildirs, which writes search results to a new maildir, which i can read in mutt.