So much misinformation (which is way the credit reporting industry prefers it). For some good articles go to msnmoney and check the credit articles. Other good articles can be found at bankrate.com - some are linked at pgary's website. Here is what we know:
(1) If you apply for a card, a hard inquiry will appear on at least one of your credit reports. But prob. not all 3. I just applied for a CitiAA Business card, it only dings my Experian report, not the others. So your scores may not drop at all due to the inquiry.
(2) An inquiry, by itself, does not necessarily lower your score. It depends on how many applications you make, how many accounts you have, your available credit, etc. If you have several inquiries over a short period, i.e. one month, your score will probably drop, but not by much. And of course mortgages are treated differently - the score system will assume you are shopping for a mortgage and doesn't penalize you.
(3) The higher your score, the less likely a single application will affect it, particularly if you haven't applied for anything in the past 6 months.
(4) Hard inquiries stay on your report for 2 years, but from what I can tell (frequently checking my score) they don't have much effect after 1 year.
(5) In the case of the OP, adding a card to the 4 you have might temporarily decrease your score but the effect is temporary. Note this will happen in all 3 credit bureaus as your account will be reported to all 3 (even if they only inquired at 1 when you applied). If you use the card but keep the balance at <30% (even better <10%) of your credit limit, your score will actually rise after a few months because you will have a lower credit utilization ratio.
(6) If you already have great credit and 6+ cards with high limits and low balances, an additional card won't have any noticeable effect on your ability to get the lowest interest rate for a mortgage or car loan.
(7) The people who have to be very careful are those with middling credit, as a drop of 10-25 points could put you in a new rate class for a car loan or a mortgage. If you are planning to apply for either in the next 6 months, you may want to run your credit score before applying for that new card. 25K miles won't be much consolation if you end up paying a higher interest rate on a jumbo mortgage.
(8) If you have bad credit, an inquiry will hurt you more initially but after time will help your score even more. But if you get 2+ cards, it will really hurt you as the system assumes you are loading up on credit because you need cash and therefore are a greater risk than someone who doesn't need new cards.