I opened a few Marriott cards to cash in on the points for a big family vacation.

What happens if I close those cards this year? Will it adversely affect my credit score, despite the fact that I've other longstanding credit cards with no balance (which I hear is more helpful to your score)?

All I can say is that I have opened and closed a couple of Marriott Visa cards twice a year for the last 2 years, plus the same with some AA Mastercards as well. I just checked my rating and it is about 800. My understanding of which is a pretty good credit rating.

So I doubt that opening/closing a couple of credit cards within a year, by itself, will cause any major hit to your credit rating.

Your credit is 'hard pulled' once by the bank when you open the original credit card. They hold your credit report on file for up to 3 years. All subsequent checks by the same bank will be done on the file on hold. So your credit report does not see these inquires.
Your credit report is based on many other factors also, such as total amount of revolving credit, total credit outstanding, amount carried every month on credit cards, etc. So churning a lot of credit cards does impact your credit but not as much as you would think.
Just read the fine print on these cards, a lot of them require that you hold them for a minimun of 6 months or they will take back the points.

Cheers

I think is very safe to say that you can close the account. I also have been doing it for quite sometime also.

As far as a hard or soft pull ie one that doesn't show to other creditors. It all depends on the particular bank. Banks based in Delaware are not permitted to retain the credit reports on file for that long. Some banks may be based in places where they are allowed to. However, the key answer to the question is that it totally depends on your overall credit report and how often you open and close an account. A person with an extensive credit file of excellent accounts can open a new account every 4 months and close one every 6 months with no impact on their score that is significant. You must determine if you fit into that criteria. Example 20+ lines of credit with 70% over 5 years old, A mortgage and car loan, 2 to 4 active lines of revolving credit v/mc/ax, the rest paid off or closed, all balances are less than 70% of your credit limit on average (more is ok with a mortgage, less is better with a credit card), department store cards are not that good for you so it is better if they are paid off or carry very very small balances.