It's pretty common for people to include photos with their tweets on Twitter, even though they have to go through a third party hosting service to do so. That won't be the case for long, as Twitter is set to roll out new photo integration in the coming weeks.
When it's all set, you'll be able to upload photos directly via Twitter.com as well as the services mobile and desktop apps. They won't be hosting the photos themselves, however; Photobucket will handle those responsibilities.
They'll also be unveiling a beefed-up version of Twitter search, which should deliver more relevant searches and trending topics as well as photos and videos alongside your results. So we all have that to look forward to!