How do large enterprises currently share files?

At Microsoft, teams have dedicated machines for content sharing over network.

There are a wide variety of enterprise level file transfer solutions.  These generally come under the banner of Managed File Transfer solutions (see http://www.pro2col.com/solutions/managed-file-transfer/) and there are a large number of vendors competing in this space including: Accellion, Axway, Biscom, Globalscape, Ipswitch, Jscape, Linoma, OpenText, Tibco and many more. If you've got a specific requirement get in touch via http://www.pro2col.com

They typically use multiple different technologies. There's an entire market of file sync and sharing services, but most end users (statistically speaking) are still using email as the dominant way to share information, although file sync and share usage is growing (from 5% of users in 2010 to 25% of them in 2012, according to Forrester). Within that category, there's a high frequency of "rogue" or tacitly tolerated file sync and sharing (led by the ubiquitous Dropbox) - according to data from Palo Alto Networks, their average customer has 13 different file sharing services in use on their network. Wanting more control and standardization, many large enterprises have rolled out enterprise file sharing technologies, especially in regulated industries. However, SMBs and mid-sized companies have been quicker to roll these out, as they effectively replace tools like SharePoint and infrastructure like storage technology at smaller firms.

File transfer gateways eg http://www.accellion.com or tumbleweed etc (assuming you mean external B2B and B2C etc) Facebook use accellion eg https://files.fb.com/courier/web/1000@/wmLogin.html and many bank and gov customers use tumbleweed

ShareFile is a secure file sharing service built strictly for businesses, so it has the security features that big businesses require: http://www.sharefile.com/enterprise/

Enterprise companies are using companies like https://www.smartfile.com/enterprise/  to share files on a global scale. SmartFile offers file sharing and management tools through an on-premise devices that can leverage existing enterprise infrastructure and provide more features than file sharing (compliance, security, monitoring, user management, access restrictions, virtual links, email notifications, and more). SmartFile is a global enterprise solution for large organizations with multiple offices and thousands of users.

A lot of companies have problems with secure file sharing because they use Microsoft Outlook. Accellion has actually solved this problem and enables business users to securely send files, up to 2GB per file, directly from Microsoft Outlook. Files are offloaded from the email system, freeing up email bandwidth and storage.   All file sharing is tracked and logged by the Accellion system. The plug-in also provides flexible end-user controls including the ability to set the file link expiration and control file access if enabled by the IT administrator. http://www.accellion.com/sites/default/files/datasheets/Accellion_Microsoft_Plugins_datasheet.pdf

Typically it is mail for most of the small files. And unfortunately for some large files too. But preferred method for small and large files is through shared network storage (NAS or SAN). Content Management systems like Sharepoint are also gaining lot of traction mainly because of access control and versioning.

We used to use Dropbox, Google Drive, and other semi-free file sharing services. But it was a total mess and nobody knew which files and folders was shared with who. Instead we switched over to using  https://filecamp.com/lp/professional-file-sharing/ for all our business file sharing tasks. Highly recommended, and our customers loves it!