It has mobile counterparts. The copy/paste part is Ok, the syncing depends on the clients. I think syncing is always through some other service, some apps claim a nice integration with dropbox, some are more tedious (I use miniKeePass on iOS and it's not fun to sync), but you won't have any fees other that what you pay for dropbox or some other third party storage.
Overall keepass is far from perfect and lacks polish, but it's good enough for most purposes, and doesn't require an internet connection, which opens more use cases (keeping banking info or wifi passwords for instance)
Overall keepass is far from perfect and lacks polish, but it's good enough for most purposes, and doesn't require an internet connection, which opens more use cases (keeping banking info or wifi passwords for instance)