20-Year Prospect
Throughout history, people have collected stuff. Some collections contain paintings by Picasso, and some collections contain pogs. You, thankfully, tend to get stuck with the Picassos, but museums are finding new things to collect all the time...which is why you'll still have a job twenty years from now.
Take the rise of Rapid Response Collecting at London's Victoria and Albert Museum. Instead of pursuing tapestries or sculptures, curators in the Contemporary Architecture, Design, and Digital Department obtain objects that are very much a part of the "now," like an anti-homeless spike (ouch), a pair of Katy Perry-branded fake eyelashes, and a stuffed animal from IKEA.
We'd rather curate Impressionist paintings, but, hey, maybe we're just snobs.
And then there are the curators who—thanks to the rise of the Internet—curate information instead of things. Biocurators, for example, collect and collate biological data. Digital curators might be responsible for managing an archive—of photos or church records or musical scores—online.
In other words, you as a curator may find yourself branching out in all sorts of unusual directions as time goes on. But, if New Age curating doesn't float your boat, you should always be able to find a museum with some dinosaur bones that need to be sorted through.