Most cloud services offer free storage to a point, which is often right around 5GB. Once you hit your data cap, though, the attraction of a freebie quickly loses its luster in the face of frustrating limitations.
For example, Internet photo stalwart Flickr does indeed offer free storage. However, you're capped at 300MB of data per month. Depending on the size of the files that your camera creates, that could be fewer than 100 images. Furthermore, Flickr lets you display a maximum of 200 pictures for public viewing. This is just one instance of a company that stunts its free offerings in the hopes that you'll ante up for a paid service.
Yet, if you plan to push your photos into the cloud for years and years, you'll likely wind up opting for a paid account. The good news is that storage pricing is typically very reasonable; the average annual cost for most is well under $100 and often close to $50 or even less.
Still refuse to pay for your photo play? Don't overlook the obvious. Facebook, for example, doesn't restrict the number of images you upload, although it does put a 4MB limit on image size. Sites such as Snapfish and Shutterfly also offer free, unlimited uploads. These services are sometimes tied to products such as prints. SnapFish, for one, requires you to buy products at least once annually to prevent deletion of your images.