Mozy is not an alternative to DropBox but perhaps useful to keep this reference to Mozy here for those people who may be uncertain of the differences.
For the record, I use Dropbox and Mozy for the purposes they were each intended.
DropBox requires proactive intent to make a file or folder available across the sync'd computers and on the web site. As soon as a change is detected in the contents of the Dropbox folder, the sync is started. On a LAN this sync'ing is almost instantaneous. One excellent use for for DropBox is in gathering together screenshots from multiple computers, using a tool like Jing or Snagit, e.g. for inclusion in a document or blog post. Dropbox makes this so easy.
Another big difference is that a single Dropbox account allows sync'ing across multiple computers (that's the whole point, after all), whereas Mozy is one license per computer.
Mozy is not intended for frequent access to the backed-up files. It is primarily a system recovery tool. Recovering files is no where near as convenient as with DropBox, but that is OK as it's not something you expect to do often.