I am a software developer where some of my work also include web development. I find IT jobs in general are deaf friendly. As long as your skill set is strong your ability to do your job is more easily proven.
I communicate almost exclusively by email and written messages. I have a captioned phone and videophone but find that I don't need to use that much. Most of my work is done on my own so it does not matter if I can't follow the chitchat which is non-work related anyway. I am fortunate that my department is small. Even in situations of large meetings there are always handouts or slides that I can follow the topics of conversations. In these larger groups, I find that few really pay attentions and it just management throwing out figures that don't matter to the day-to-day work - so no big deal if I am not getting it all. I have a good buddy that let's me know if there were any big announcements that I might have missed.
I find that if you are looking for a job, while smaller companies may have less experience with deaf employees they may be more willing to take a chance as their hiring process is usually less bureaucratic than a big company with a large HR screening processes that may screen you out before you have a chance to meet the person you would actually be working for.