Allergies: Excessive scratching to the point of bleeding; watery eyes.
Cancer: Increased thirst, change in urine habits, vomiting, diarrhea or constipation, sudden weight loss or gain.
Diabetes: Increased thirst and urination, increased hunger or loss of appetite, weight loss or obesity.
Kidney disease: Increased thirst, increased urination, vomiting.
Periodontal disease: Dirty teeth, bleeding gums, loose or missing teeth, avoidance of touch near mouth and cheeks; lackluster or oily coat, dandruff, excessive shedding, bad breath. These could be signs of other illnesses, as well (cats should never have bad breath).
Urinary tract infection: Urinating outside the litter box, blood in the urine, excessive genital licking, squatting and crying.
Vomiting can signal digestive discomfort, for which cats often eat grass; the fiber stimulates vomiting, which cleans the intestines. Sometimes the cause is competitive eating in multicat households.