/home on a separate partition is fairly common. That typically splits system files (
/) and user files (
/home). The two filesystems may have different performance trade-offs, different backup policies, different quotas, different security policies, etc. Also this way the OS can be reinstalled or reimaged independently of the user data. Splitting
/home is a good idea both for single-user workstations and for multi-user systems that store user files. I'd only keep
/home on the same partition on a server that has no user files beyond the administrators' configuration files (but there might be a separate partition for whatever that machine is about —
/var/mail, or a database, etc.), or on a quick-and-simple installation especially on a laptop which isn't going to be rebalanced to use a second disk.
/usr on a separate partition used to be common, back when the OS used a large amount of disk space (say, 300MB out of 1GB). This partition could be made read-only, might be shared over the network. Making
/usr read-only had the advantage that in case of a power loss, it wouldn't need an fsck. Nowadays all major filesystems use a journal and don't require any lengthy fsck, and disk sizes have increased a lot more than OS sizes — 30GB out of 1TB is peanuts, so it doesn't need to be shared. There is no good reason to split
/usr from the rest of the system (
/var, …). If you see advice to split
/usr, it's grossly obsolete.