Medical Issues

The Kilimanjaro National Park authorities have set a minimum age of 10 for climbers, although some operators discourage anyone under 13 or so from climbing. There is no upper age limit to climb, and in fact people in their 70s and 80s often climb and make the summit.

Everyone planning on climbing Kilimanjaro is encouraged to get a physical in the weeks leading up to the trip, and anyone over 60 or in marginal condition is encouraged to get a physical before fully committing to the trip. Older climbers often do better than their equally-fit and younger counterparts, but this is serious business so you need to be careful.

If you are climbing any mountain - not just Kilimanjaro or Mt. Kenya - you should always keep this in mind:

Do not go higher than 10,000 feet if you have any of the following conditions:

nose bleed
cold
sore throat
Respiratory infection
High Temperature
cough

From time to time on Kilimanjaro, you might wake up with a sore throat or a small cough, and if it persists for more than 24 hours you should get down the mountain as soon as possible.

Generally, people start feeling the effects of altitude above 10,000 feet:

Here are the common medical issues people face while climbing Kilimanjaro:

AMS — Altitude (Acute) Mountain Sickness

Symptoms - headache, loss of appetite, tired, vomit, dizziness, sleep issues
Remedies - descend, Diamox

HACE — High Altitude Cerebral Edema

Symptoms - AMS first, severe headache, confusion, stumbling, behavior change, coma
Remedies - descend, chamber, oxygen

HAPE — High Altitude Pulmonary Edema

Symptoms - AMS first, easy tiring, dry cough, difficult breathing, lung crackles, death(!)
Remedies - descend, chamber, oxygen

In addition to your normal First-aid kit you should consider the following:

Diamox (Acetazolamid) 125mg/day before ascent, 250mg/day upon start of illness
Gamow Bag or Hyperbaric Chamber
Stethoscope
Codeine, Cipro, antihistamines, cough drops

Diamox and you

Most Americans want to use Diamox while climbing Mt. Kilimanjaro. There are different opinions and perspectives on if you should use it and how you should use it. Here is a sample of good links where people debate the subject and if they had positive or negative effects with using Diamox.

Altitude Sickness and the Side effects of Diamox
A good discussion thread on Diamox
Wikipedia on Diamox

And finally:
How to Get Diamox for Altitude Sickness

Malaria
Malaria Prescriptions