Occasionally, I get asked "don't all those new cards kill your credit score?" The answer is "not really." Gary over at View From The Wing has a very good post that explains it all.
Basically, a new application that results in your credit report being "pulled" will cause a temporary drop in your credit score (usually less than 10 points). However, getting approved for a new card might actually raise your score by decreasing your credit utilization level. My score is comfortably over 800 despite having applied for and received around six new cards in the last year.