Can you leave Thailand freely on a Non-O Marriage Visa?

As you please doesn’t translate into Thai (Joke)

Leaving isn't the problem. It's getting back in.

depends your wife.

Only when you carry a permission note from your wife :-p :-p :-p

[inserts satire here]

It depends on where you get a visa. If you get your Non O from overseas, your Non O visa will include a multiple entries permit. However, if you obtain a Non O visa in Thailand, you must apply for a multiple entries permit after you get the visa and before leaving Thailand. If you don't have a multiple entries permit, your visa will be set back as a single entry and you have to start the process all over again to get a visa when you come back to Thailand.

If you are on a Multiple Entry Non Immigrant O visa based on marriage with a Thai National you can leave and come back until the valid until/Enter before date on the visa. If you entered Thailand with a Single Entry Non Immigrant O visa based on marriage with a Thai National and want to leave and come back during the 90 days of stay you need a re-entry permit. If you have an Extension of Stay based on marriage with a Thai National, from Immigration office you need a re-entry permit as mentioned in the stamp in your passport.