DI wrote:
How many is too many? It depends on the creditor who you're apping for a card with. Some like no more 3-4. While others don't seem to mind how many inquiries you have if everything else is looking good in your credit reports. Chase is one creditor who do not like a lot of inquiries. Just my credit cents!!
In a great example of how YMMV, I was approved for the Chase Freedom Visa last month with 12+ inquiries 
I think the answer to "how many is too many?" -as ambiguious and unsatisfying as it might seem- is "it depends".
Just based on common sense though, I tend to agree with another poster who said when you start getting denied, that's too many.