I am building a large database for my analysis tool ~3 Terabytes.

The issue is distributing this database for people to use it.

A solution we have learned from working with sequencing cores is to ship a hard drive by FedEx.  A possibly expensive and annoying proposition.  

Another solution is to host the files for download, but this seems possibly expensive or possibly impractical for the audience.  (On this point of practicality -- most Universities have gigabit level bandwidth, perhaps 3 Terabytes is no longer a ludicrous download size, simply a big one.)  At 1 gigabit, I estimate the download would take 400 minutes.

Since this is a niche' problem, I am hoping someone may have had a similar issue and can provide advice?

Thank you
Jeremy Cox
Shipping disk is the most reliable solution once you've reached the TB range. The problem with sharing over the network is that the speed is only going to be as high as the network bottleneck between the two ends (including bottleneck inside the institutional networks) then there's some overhead depending on the protocol. Also the connections are often not stable over the many hours (up to days) required to transfer a large data set so you need mechanisms that can automatically reconnect and resume where the transfer was interrupted eventually replacing files that were corrupted when the connection was lost. There are technologies for large data transfer over the network (e.g. Aspera, GridFTP) but you end up running into costs and deployment issues.  
You should also consider not transferring the data. Maybe you can provide local compute to your collaborators or allow them to extract relevant subsets and only transfer those.