Number one would obviously be to connect to two different networks. It could also be useful in a scenario where the machine is used as a server and you want a semi-redundant backup network line. It could also be used to directly connect to a NAS box via Ethernet.
[0] by real world I mean on a properly configured network. Many companies don't have that though so you often see "gigabit" speeds in the 30-50MB/s range.
10gbps is expensive, uses a lot of power, requires cat6, and rare outside of servers and SANs currently. Interestingly enough, there's a recent 5gbps spec that works with Cat5e that might be picked up by OEMs to replace 1gbps. Still no chips or cards out yet, so it will probably be a while. In the meantime, bonding two 1gbps interfaces gives you about a 200 megabyte/sec write & read speed off a SSD based server/NAS.
40GbE is probably overkill, right?
Not at all. :)
If you're working on video over the network you can use two ethernet cables for faster network access