Dropbox/Google Drive work on the principle that when a file gets modified, it will upload the file into the cloud. Then when your on your other machine, it will download the latest copy.
This works great for small files.
- GIS data can often be large filesizes.
If I edit one feature attribute in a layer that is 2GB big, there will be a lot of uploading/downloading of that file.
- GIS data is often accessed by more than one user
Conflicts would occur if multiple people using the same dropbox account and trying to edit the data.
Sounds like your goal is to sync projects between work and home.
If your working on projects that involve <250mb size datasets, then the dropbox/google drive account would be ok to sync your project between multiple locations.
If the filesize gets bigger, it might be easier to sync the two locations with a external hard drive and a tool like SyncToy.
For most organisations, a RDBMS is the usually best approach for syncing and backing up data across multiple locations. If you only edit one record in a large dataset, there is no need to sync the entire database to a separate location, but just trickle to differences across. See Esri's GIS Data Administration for more details on this.
If need be, a RDBMS can also be held in the cloud -
e.g. Using Windows Azure SQL Database and ArcGIS