The biggest factors in helping your credit score are no late payements (or worse), long length of credit history, and low utilization (not using too much of your total credit limit).

If you already have had some credit cards for a long time, still have those open (so the credit history continues), and have low or no balances on your cards but high limits, then applying for new cards is only going to affect your credit score in small and temporary ways.

And cancelling those cards (after the bonus posts) won't hurt either, since they will be cards with short credit history. It's cancelling cards that you've held for many years that hurts your credit history. (Those you want to "consolidate", if you have more than one with a particular issuer, rather than cancel.)