Thought I'd add a data point for Chase. I applied on 2/21 for the Amazon Visa and the United Explorer card. Both were pending (I did not call) until today. I came back from a meeting and had a missed call on my cell and work phone from Chase. Logged in online and had two new cards that appeared! I'm at my max exposure with Chase already so they reallocated some of the limit from my Marriott card to the Amazon - they pulled $9K from the Marriott to the Amazon. The twist is that they closed out my Freedom card and moved the entire credit limit to the United Explorer card...all $19,500 of it. I didn't ask them to close the Freedom so that's something new. In the past they would always just reallocate some of the limit from one card to another; however, I'd only applied for one card at a time before.
I called after work and spoke with a CSR - she attempted to reopen the Freedom card but told me to call between 8A-5P tomorrow to speak to the department that could see about getting the Freedom re-opened. I sure hope they can; has anyone else had that happen? I had four total cards with Chase prior to the approval. Either way I'm glad about both approvals 
Fico scores at the time of the pull (they pulled EX and TU). 785 on EX and 804 on TU. I've got 30+ inquiries on EX and 12 on TU. Accounts opened in the last year prior to these cards sit at 10. I have a pretty deep file and lengthy history (15+ years) with no lates. I've got all the cards I want at this point so don't see myself going for much more in the near future unless a nice sign on bonus presents itself.