Please be carefully when you use such services. For example Google Drive has some things in their terms which might sound as Google would own the files (please see yourself, i just heard that).
What I recently discovered and what looks pretty good is Spideroak:
Besides that personally I like plain old E-Mail. It has every feature I need. For important documents I do sign and encrypt my E-Mail. Then it is guaranteed that nobody else does read it - even not any third party like a file transfer hoster. There are tons of instruction how to do that:
SpiderOak is a zero-knowledge encrypted data backup, share, sync, access and storage service. Online and multi-platform with 2GB of storage free for life.
https://www.google.de/search?sugexp=chrome,mod=5&sourceid=chrome&ie=UTF-8&q=signing+and+encrypting+emails There is good software available, like the classic PGP the open source variant GPG. Also there is S/MIME. CaCert does give you certificates for free. For all these services do plugins exist for Outlook and Thunderbird.
Your question is somewhat vague. Are the files for processing (e.g. data file for online reporting system) or are we talking about adhok documents such as legal paperwork?
If the former, then go with the flow and get yourself an SSL certificate - banks use them, it has never been hacked.
If latter, then there are various online services (such as dropbox/googlefiles/etc) or just use PGM or something similar and email encrypted files - even encrypted zips are very secure in real terms - sure thousands of computers can hack it in a day or so - is this likely to happen to you???
Users can upload documents of up to 10 GB in size to Google Docs. But users also only have 1 GB of free space available. If you want more space, you have to buy it. But since many users have Google accounts, this could be a good option for your needs.
More info on space availability on Google Docs: https://support.google.com/docs/bin/answer.py?hl=en&answer=37603
I'm a lawyer and smaller companies typically send deal documents on Dropbox.