I have limited experience with Dropbox, but I have successfully used it for creating galleries and image delivery for clients.
I think it depends on what you expect from such a service. Do you want something whereby you can visually browse images in galleries, or is a simple structure of folders containing files without image preview sufficient?
An option could be Flickr as they're now allowing 1TB of free storage, IIRC. And you can browse and organize images visually. While it's set up as a social site with the ability to share, you can set privacy settings to prevent others from seeing your images.
Photoshelter is a more 'pro oriented' version of Flickr that will allow online commerce, etc. But it also has a lot of tools for storage and organization. The price reflects certain aspects beyond simple storage.
Google Drive is a pretty good consumer solution for image uploads and storage. They give you 15GB free per account (you can sign up for as many as you want, it seems). Otherwise you can buy 100GB for $24/yr or 1TB for $120/yr.
Then there is something like Amazon Web Services' S3 (Simple Storage Service). This is basically a pay as you go, pay for what you use, FTP-like service.
http://aws.amazon.com
You can interface with it using their online console or by any FTP app that supports S3 functionality.
IMO, advantages and disadvantages of each:
Flickr:
Pros:1TB free. The social aspect. Decent functionality. Ability to caption and add other metadata tags.
Cons: Accessing/downloading large quantities of files (i.e. to recover those lost locally) is slow. IIRC, it's pretty much one by one download. It's not a system really designed for getting stuff off the site and back onto your hard drive (based on the last time I looked a while ago... things may be different now?).
There's also the need to police their terms of use in regards to access by 3rd party partners and other 'behind the scenes' privacy details. There has been some uncertainty about what Yahoo! plans to do with Flickr...
Google Drive:
Price is OK and it's easy to set up directories of images and view them as galleries. Options are available for sharing files/galleries with others who don't require a Google account to do so. On the downside, the service is occasionally a bit flaky - i.e. galleries don't display properly or clicking on a thumbnail doesn't show a preview or allow access from the public side of shared galleries. If there is too much download traffic on the public side, access will be suspended for ~ one day. Logged into your account, you're able to batch download 2GB at a time, though I'm not sure if there is a daily limit, etc. Huge directories (500+ images) are problematic. Better to break things down into more manageable sizes. Google should be around a long time, though they have the habit of abandoning, or drastically changing services.
S3:
Pay as you go. Uploads are free but there are monthly costs for total data on the service, as well as for traffic accessing the files and downloads:
http://aws.amazon.com/s3/pricing/ You can use S3 for file hosting (i.e. posting on forums, in your own website, etc.), though you will pay for all traffic accessing such linked files, which can add up. As an example regarding storage, I have probably around 200GB on S3 at the moment and am paying just over $7/month. While a couple paid 100GB Google Drive accounts would be cheaper, I like the simplicity of S3 and the ability to upload and manage it directly via ftp. BTW, Amazon constantly reduces S3 storage costs. It's about 1/3 of what it cost ~4 years ago, though download bandwidth costs seem to have remained fairly constant. For truly longterm archiving, Amazon also have a cheaper and much slower (to recover files) service called Glacier. From S3 I can quickly and easily download as many or as few files as I want, without any traffic limits. But downloading files is also the most expensive aspect of S3... Many, many cloud storage services, web sites and other online services are built on Amazon's Web Services. Amazon caters to corporate/business users (but small fish like us are equally welcome), which means they're in it for the long haul where reliability and availability is highly critical. They're not likely to arbitrarily change significant aspects of the service on a whim.
My current cloud implementation is to backup final edited selects from everything I shoot - these are the final processed files - to both S3 and Google Drive. I don't currently back up original RAWs, PSD working files, etc., unless they are of critical value. Cloud storage is for me a 'last resort' backup in case of disaster relating to my multiple physical backups. It's also useful for accessing files while away from home. Maybe not as relevant to you, but handy when a 'client' (a paying one, or a relative, etc.) can't find certain images but needs them ASAP.
There are certainly many cloud storage options out there and the above aren't necessarily the best solutions for everyone. You'll definitely want to compare them against Dropbox.
One thing I would also strongly recommend is to consider longterm viability of such services. As mentioned, there are many players out there... How many will still be around in 2, 5 or 10 years? This is where shopping strictly based on price could be a problem. Pay a little more for something like S3, but in exchange receive peace of mind that the service won't suddenly disappear with all of your images into the ether. For an example of this, look up Digital Railroad...
