Users participating in the private beta of Google+ have probably noticed the direct connection between G+ and Picasa for photo and video storage. Considering this, Google revamped the storage plans for Picasa, allowing G+ users to have unlimited storage space. Well, almost unlimited, that is. Up until recently, Picasa Web Albums had a 1GB per-user data cap, but now, G+ users can upload any photo smaller than 2048x2048 or video shorter than 15 minutes without it counting towards to the 1GB cap. Fortunately, if you upload your photos with G+, they are automatically resized, so they won't take up any space in Picasa, whereas photos uploaded directly to Picasa will be unaltered, regardless of size.
If you aren't part of the G+ private beta, don't fret - you're also getting unlimited storage, albeit not under the same circumstances. For photos, you're only allowed to upload photos up to 800x800 without taking up any of your precious Picasa space. Like G+ users, though, you can upload videos up to 15 minutes in length.
If 1GB still just isn't enough space (or you have tons of huge photos and large videos), then you have the option to buy additional storage from Google starting at $5 per year for 20GB.