SFS
Central file server services

Per group:
$9/mo for 150GB
$30/mo for 500GB
$60/mo for 1TB (onwards)

http://www.it.cornell.edu/services/sharedfile/fees.cfm

Service backs up all files there via EZ-Backup at no additional cost.
Versioning (access to prior versions and deleted files) is available, and obviously takes up some  of the allocated space (~20%).
Set up private folders for each member. By default, can't see each others files.
Has capacity for shared folders and documents, if sharing is desired.
CIFS are Windows and Mac-friendly. (NFS option also available.)
Accessible from off-campus via VPN.
NetID-based so usernames and password are easy to remember.
If you need more than 1-2 TB of storage, other solutions may be more cost-effective. Contact ChemIT for more details.

EZ-Backup
Central backup services

Per computer:
$5.50/mo
(First 18 GB, compressed)

http://www.it.cornell.edu/services/ezbackup/fees/

Default setting is to backup full computer, including the OS, which makes for a larger backup and thus potentially more expensive.
But the most cost-effective method will requiring carefully and accurately focusing backup on just user's unique docs, not full OS.
There is an archive service available.
A cost-effective solution for even larger amounts of data on one system.
Very robust backup services, well-proven over the years.

Box.com
Central cloud storage

Free to CU members, up to 10GB
More data, via formal request.

http://www.it.cornell.edu/services/box/about.cfm

Good for working files. Good for sharing, including to your own, other computers. Limited space.
Individual file size limit is 2GB.
Limits on file names and path lengths.
Cornell-contracted. Use and rights governed differently than with your group's private DropBox.com accounts, for example.
More space may be available to individuals; contact ChemIT to explore this option.
Has capacity for shared folders and documents, if sharing is desired.
Service stores prior versions of files, and in most cases also deleted files.
Consider backing up files in case account gets hacked or of a bad internal actor.
NetID-based so usernames and password are easy to remember.