There are many services for storing and sharing your photos online, but if you want to get really serious about turning your photography into a profession, then take a look at SmugMug.
SmugMug is aimed at pros, and lets you not only store and profile your work, but also sell directly through the site. Other sites can do this, too, but SmugMug really has a great approach and understanding of professional photography. Even if you aren't eager to sell your work, SmugMug is one of the best polished photo-storage services around, so it's well worth a look. The basic plan is US$40 per year, and that allows for unlimited photo storage. It's a great deal, and a great web service.