Different companies have different criteria for assessing who's a good/bad risk to lend to.

I recently requested a copy of my credit record, and it does show when you've applied for credit in any form (credit card, home loan, mobile phone account etc) but doesn't indicate whether your application for credit was approved or declined.

I imagine if you'd applied for a number of credit cards (or other lines of credit) in quick succession it might be offputting to a potential creditor - It could like you either have too much debt (and may not be able to keep up with the repayments), or you keep being declined credit, neither of which looks good.

OTOH, assuming you don't have a whole suite of credit cards/loans etc already, applying for one new card IMO is no big deal.