Smartphones can do the job, and new services make it a lot easier than previous options, which are complicated and slow. Nobody wants to configure a VPN connection on a smartphone, and browsing a directory structure on a remote server over a 3G connection can be brutal.
Now, companies and individuals often have an online backup program or some sort of document replication service that keeps files in sync between a cloud and multiple computers. The solution is to access those files stored in the cloud from your phone. Browsing is fast and the client software is easy to use.
Mozy has had a Pro service for several years that is designed to allow IT personnel keep client data backed up no matter where in the world that client computer happens to be. Mozy just announced an app that allows users to access their MozyPro data from either an iPhone or an Android device. If you administer MozyPro backups for your organization, you can disable this app from the administrator panel if desired.
Mozy isn't the only service that allows this. Both Dropbox and SugarSync have clients that allow you to retrieve files from a cloud account. Dropbox supports the iPhone, iPad, Android, and Blackberry clients. SugarSync does all of that plus Windows Mobile--but not Windows Phone and Symbian.
Additionally, SugarSync has a business service that allows multiple users to share and access folders you select and control all of it with password and permission settings.
Not only do these and similar services allow employees to access their files when on the go, they provide a robust offsite copy of corporate data, often with versioning and the ability to recover deleted files. The clients are easy to install and at most, requires poking a few holes into a firewall to allow them to operate. No VPN clients necessary. You can read a review of some of these services here.