I have always been worried about paying off accounts prior to a round of applications, but it hasn't seemed to matter.

This is with a ~780 score, $120k total credit, with about $9-10k of balances (most of it on one card, a 0% offer with 80% utilization). I have a 13 year credit history.

I was approved for 5 cards last week (Amex biz platinum, ink bold, US air, AA platinum, United explorer) and 2 cards in January (Amex platinum, sapphire preferred). All were instant except for Chase, which had me reallocate some credit and approved.