Currently we back up about ½+ TB to disk and then that goes to tape, as it
takes too long to go straight to tape.   Dropbox at $240/year for 100GB
would cover a fair amount of data, but would that solve more problems than
it would create?  Amazon can host all of our backups for about the cost of
our tapes for 1 month… but can we even begin to push that amount of data up
to the cloud with a tiny 30MB handoff?  How big a pipe do we need to
realistically use these solutions and will that cost be worth it?

Say 600GB of data:

600GB = 600,000 MB * (8 bits/byte) = 4.8x10^6 Mbits / 30Mbps = 160,000
seconds = 44.5 hours.

If 5 hours was a requirement (common for direct-to-tape), you'd need 270Mbps
dedicated to your backups, plus line overheads and other usage. Call it a
300Mbps connection, but only for your 5 hour window.

If 24 hours was an option (local disk buffers and Sunday pipe usage), 60Mbps
could work.

Any connection will have TCP (4%) or crypto 3DES/AES (15%) overheads on the
connection, plus any control traffic for your data streams. If you are using
your connection for other stuff at the same time (regular Internet usage,
VPNs, remote classrooms, etc.) or the file host won't accept at that high
data rates, your connection will need more time to finish the job.