Personally, my wife & I both have great credit: >750 on Experian's Plus as of about 2 months ago (my wife still wonders how I get that high because I've churned about a dozen cards in the past 12-18 months).

She was denied by Discover and Chase recently for "insufficient credit history" even though she's never missed a payment and has had 2 cards open for over 8 years. More recently (past 2 weeks), I was denied by Chase twice for "insufficient credit history" and "too many credit inquiries." I've had tons of credit for up to 15 years, so I think they're BSing. Personally, I think Chase just cut us off because we've gone through the BA card, Priority Club and UA cards in the past year and I still have about 35k in available credit from them that I'm barely using now that the coins are done.

However, AmEx approved me for credit today. So in short... I'd say where you draw the line isn't clear. Just don't over do it with any one company in a short period.