To summarize HikerT somewhat:
- banks care about the number of hard inquires a lot (too many in a short period and they worry you've befallen some financial hardship)
- banks look at the percentage of your total credit usage/credit limit ratio. Too high and they worry what additional credit will do to your ability to pay
- average age of accounts matters a little- keep all your old no-fee cards.
- above all: pay your bills on time!

Also remember if you are initially declined you can call or write for reconsideration. I applied for and was approved for the SPG, Chase CO, US Air, AA Citi Personal, Chase BA, and Cap One Venture card in a 3 month period.

After 3 months (last week), I applied for the Sapphire card and was initially declined. I called the reconsideration line and after being denied again twice by the agent and once more by his supervisor, she finally relented and gave me the card.
** she wouldn't give it to me without closing another card, but since I had already cashed in the CO Chase points, I closed that one to get the Sapphire card.