You don't have too many cameras. Not yet anyway. [Updated with Question: how many different camera models were ever made?]
You may think you have too many cameras. Your spouse may think you have too many cameras. Your friends and family and co-workers and frenemies may think you have too many cameras. They are all wrong! You do not have too many cameras!
Unless you are Mumbai camera collector Dilish Parekh. He has 4,425 cameras. A world record. Breaking his own world record.
UPDATE: this also raises an interesting question. How many individual camera models have been made so far? Over 10,000? Over 20,000? What is the Mumbai collector's percentage of all cameras ever made? Granted, a definite number may be too difficult to come up with when you factor in different variations and different names and brands around the world, but still, someone must have come with a ballpark?
For digital cameras, it is easier to come up with a ballpark estimate. Probably over 2,000 (very rough estimate) from the major camera manufacturers alone. For film cameras, estimates are a lot harder to come up with...
...but surely, if a bird-brain like me can think of this question, surely someone has already thought of it and came up with an answer???