Are there credit cards, as for online shopping only, that one can apply to online and get the card number immediately, without waiting for a physical card to arrive via snail-mail?
Most card issuers will not offer "instant credit", because it increases the risks from fraud; requiring both a delay of several days and requiring you to retrieve the card from the mailing address makes fraud less beneficial and more difficult.
Many retailers, however, do give instant credit; for example, Amazon.com offers instant credit on purchases on Amazon.com if you get their card. These have less risk of fraud (due to some of the same reasons as above - you don't get your stuff instantly, and you have to have a verifiable mailing address). There is also more benefit to the retailer (you're more likely to spend money at their store if you get their card), so they're willing to take a bit more risk of fraud.