My firm uses Dropbox for storing our files online, and I love it. If you want to have a paperless (and mobile) office, I highly recommend using Dropbox. If you elect to go paperless, you also need to invest in a solid scanner, like the Fujitsu ScanSnap s1500. Dropbox costs $9.99 a month for 50 gigs of storage, and a ScanSnap will run about $420, depending on where you buy it.
There is another option though. OfficeDrop is a new service that basically handles all the scanning for you. You can either upload documents and email them, or send them via snail mail. OfficeDrop will then scan the documents, create searchable PDFs, and store them online. You can organize files however you like, and also grant certain people access to various files. For an extra fee, OfficeDrop will also securely shred any documents you send. Click here to view the various pricing options.
If you have the money, and need the time, OfficeDrop looks like a nice service. Rather then spending your time scanning, labeling, and shredding, they will do it for you. Other then that, I see a number of problems with using this service for legal work.
One, it is not incredibly affordable, at least compared to the alternative of Dropbox and self-scanning. OfficeDrop has limits on the number of envelopes you mail each month, and limits on the number of sheets per envelope. Unless, of course, you want to pay more then the most expensive plan of $59.95 per month. There are also limits on the number of pages they will store online.
Two, what happens when you need to access the documents, but they are in transit to OfficeDrop? I suppose you could scan them yourself, and then email them to OfficeDrop, but that is not efficient.
Three, OfficeDrop uses OCR to make all the text searchable, which is really nice. But, the ScanSnap can do the same thing. Our firm generally does not do it because it takes time. But once you have a PDF, you can also have Acrobat OCR the document, if you really need to search it.