Under no circumstances would I list my hearing loss in my resume. It's just not the right place to put that type of information. The resume is where you list experience, skills, education, and awards/honors. I would, however, mention it in the cover letter (like Daredevel said) if I felt it could potentially help me get hired, but it really depends on the job and the employer.
One thing to keep in mind is that being Deaf/HoH means you are in a minority group, and some employers, particularly government agencies and public universities, will actually give you more consideration because of that. If I were applying to a job where I felt the employer was fair and that my hearing loss would not negatively affect my performance, I would definitely mention in my cover letter that I am HoH. The reason for putting it in the CL is because it gives you the opportunity to educate the employer on how to think about your hearing (rather than letting them fall back on their own biases and misconceptions of deafness). The trick is to be rhetorical and make the employer believe that hiring a deaf/HoH individual will actually benefit their company. One way to do this is to discuss an example where you have gained a special insight by overcoming communication barriers. The more closely you can relate your personal experience to the type of job you will be performing, the better. This shows the employer that you are resourceful and independent and won't be a burden on the company.It also shows that you think in a way that just might in fact be productive for the job you're applying.
This is also the case for applying to schools, and I encourage all of you soon-to-be college students to really be candid about your hearing in your entrance essays. When I was applying for undergrad, I didn't mention it, and I didn't get into any of my top choices. When I applied for grad school, I made it the focus of my cover letter, and I ended up getting accepted to my 2nd, 3rd, and 4th picks. Of course, that higher success rate was probably due to a combination of many things (better grades, writing sample, etc.) but it certainly did not hurt to mention that I am HoH.