Initially, I was thinking particularly of games such as GTAIV, Just Cause, Prototype, Crackdown and the like, which tend to be popular because of that aspect. I was going to just tag "sandbox," but while those games are usually referred to as sandbox games, they're often more accurately described with terms such as "open world"/"free roaming" or "non-linear gameplay," if you want to get wordy in your tagging.
However, sandbox/open world gameplay can also refer to gameplay in other games outside of the "third person action-adventure" genre though, though there's a ton of those and they tend to be what people think of for the term. Games like Fable, the Fallout series, The Elder Scrolls, and even driving games like Need for Speed and Midnight Club, and I'm not sure how to differentiate those in a manner that would be clear to people tagging in the future.
To add to the confusion, some games have a "sandbox mode," which often lets people play around with the game's features without a time limit, looser restraints in regards to resources, etc. People often seek guides on these modes, as they're just fun to play around in. (See this question)
Wikipedia is usually what I refer to when I need to stick things in a genre, and it uses the category Open World Video Games. I guess the main, albeit subtle, difference is that "open world/free roaming" describes the setting, whereas "sandbox" represents the style of play. Which term would be ideal?