GitHub has all the things, seriously, it rules. OKFN hosts open data there. So do I. As do most Code for America brigades. But you can also get a free datahub.io account, at least for an organization and you can upload there.
You should also check out your area. Here in Virginia, there is an OpenVA data portal, and anyone can upload related data after signing up. Google your area and see if there are any municipal portals you can hit up.
EDIT: adding more options.
check out dat data, i have considered it on numerous occasions, and i may just use it personally so i get to play with it.
which was built by okfn, and runs off ckan...
you could really get wild with free third party services: you could put them in dropbox, g drive, heroku, etc. you can also get a "free" account with amazon, not sure if its aws or as3; i do know that even though it's "free", it requires a credit card, and then i stopped filling out the application. :)
anything that gives you storage and url(s).
but then you are giving up ownership of that data. @ least to some extent. oh and now they have the data too. not like i pulled a copy of that repo, like, hey we can just walk in the front door and do whatever we want, whenever we want.