The only health concerns I know of with regards to tea are tooth staining and caffeine.
Tooth staining can be avoided by brushing your teeth with a non-abrasive whitening toothpaste, and getting regular cleanings. You should try to brush your teeth after drinking tea, but not right before (either eat something first, or wait an hour).
As for caffeine:
To experience acute caffeine poisoning, the average person would need to drink 250 cups of tea to get a lethal dose within 24 hours. At that point, you would go into hyponatremia (water poisoning) before being poisoned by the caffeine.
As for long-term caffeine effects, the AMH states that moderate caffeine consumption (300 mg, or about 7.5 cups of tea, per day) is not a health concern, provided that one leads a healthy lifestyle. If you are re-brewing the leaves at least once, that means you can drink about 15 cups of tea per day before the AMH thinks you could even start to have problems.
According to medic8.com, if you are drinking more than 10 cups of coffee (~20 cups of tea; 40 if you re-brew) per day, you should seriously consider reducing your consumption:
http://www.medic8.com/healthguide/artic ... feine.html
And, of course, you can de-caffeinate any tea by pre-steeping it for about 30 seconds before making your first cup of tea. This would mean almost unlimited cups of tea without any caffeine concern.