It all depends on your total credit profile.

If you have 20 cards with similar credit limits and close one, it's not going to be very significant. If you have 3 cards and close, that is going to be more significant.

Also, remember that at many banks, the key getting a new card is lowering, not raising (or even keeping the same) the total credit limit you have at that bank. Because a bank where already have credit looks just as much at what credit you have with that bank, as with your credit score and total credit picture, to decide whether to give you a new card with new credit limit. So from the standpoint of applying for new cards, the best procedure at many banks is to lower the credit limit on an existing card a few weeks before you close it. At many banks, credit limit that's voluntarily decreased is put back into your "pool" of credit limit (available to new card cards) within weeks or a few months, while credit limit that was on a card when it was cancelled may not be available for a new card for a year or more at some banks!

Lots of FTers have "excellent" credit scores despite applying for cards many times a year and cancelling cards many times a year. But that doesn't mean they cancel every card they have after, they presumably keep some "anchor" cards "forever" (either cards with no annual fee, or "net negative annual fee" ie the annual benefit such as free hotell night certificate is worth more than the annual fee costs).

Keeping every card (that reports to credit bureaus) under 30% utilization every month is much more significant to your credit score than an open here or a close there or a credit limit reduction there.

And, of course, never ever being late on a payment, never defaulting on a payment, and making sure than any mistakes on your credit report are corrected, are all more important than any of the above.