Can mumps really cause me to go deaf?

There are many illnesses and diseases that can cause some form of hearing loss. The extent can vary from mild to profound deafness.

Measles may result in auditory nerve damage
Meningitis may damage the auditory nerve or the cochlea
Autoimmune disease has only recently been recognized as a potential cause for cochlear damage. Although probably rare, it is possible for autoimmune processes to target the cochlea specifically, without symptoms affecting other organs. Wegener's granulomatosis is one of the autoimmune conditions that may precipiate hearing loss.
Mumps (Epidemic parotitis) may result in profound sensorineural hearing loss (90 dB or more), unilateral (one ear) or bilateral (both ears).
Presbyacusis is deafness due to loss of perception to high tones, mainly in the elderly. It is considered by some to be a degenerative process, although there has never been a proven link to aging. (See impact of environmental noise exposure above.)
Adenoids that do not disappear by adolescence may continue to grow and may obstruct the Eustachian tube, causing conductive hearing impairment and nasal infections that can spread to the middle ear.
AIDS and ARC patients frequently experience auditory system anomalies.
HIV (and subsequent opportunistic infections) may directly affect the cochlea and central auditory system.
Chlamydia may cause hearing loss in newborns to whom the disease has been passed at birth.
Fetal alcohol syndrome is reported to cause hearing loss in up to 64% of infants born to alcoholic mothers, from the ototoxic effect on the developing fetus plus malnutrition during pregnancy from the excess alcohol intake.
Premature birth results in sensorineural hearing loss approximately 5% of the time.
Syphilis is commonly transmitted from pregnant women to their fetuses, and about a third of the infected children will eventually become deaf.
Otosclerosis is a hardening of the stapes (or stirrup) in the middle ear and causes conductive hearing loss.