I prefer webmail to desktop mail, but I've traditionally used SquirrelMail. While I'd dabbled with RoundCube here and there in the past, I'm now using it regularly and so I can easily say:
Like most IMAP email clients, it can manage folders with ease. However, unlike some webmail clients, it has the ability to connect with a relational database (SQLite, MySQL, etc) to store contacts and signature information. It can also connect with LDAP servers for this!!
I'm eager to try out RoundCube plugins, particularly the managesieve plugins so that I can automatically organize my emails.
Have you tried RoundCube? What do you think?