There exists a mostly-standard X-Label mail header that can be used to attach free-text labels to mails. However, what little support in mutt I could find for this header did not work well with IMAP.
Firstly, apply this patch (from here) to your mutt installation (works for me on mutt 1.5.18). This provides the <edit-label> operation, which you can use to apply labels mails. I chose to define a set of macros that apply various pre-defined labels.
Then, optionally setup a theme that displays your labels in the index, and perhaps colours messages differently. Mine is available here. Apply this to one or more mailboxes using folder-hooks.
Finally, the secret sauce to get it working with IMAP. Since mutt doesn't understand the X-Label header natively, you need to force mutt to reload the message body in order to save and display the label changes. Do this by first syncing the mailbox, then reloading it, eg. with a macro like this:
macro index "#" '<sync-mailbox><change-folder>^<enter>' "Sync mailbox".
It's a hack, but it works.
I use the remind package for calendaring, and have a set of scripts to parse ical mail attachments into remind format. See here for details.
I routinely work out of multiple IMAP accounts within mutt. I achieve this by using account-hooks and macros to switch between accounts. See my muttrc for details.