Are DS games region locked?

It would appear that the games are not region locked according this this Wiki article that states:

"The Game Boy and Nintendo DS product lines do not use regional lockouts for physically distributed games; however, software specific to the Nintendo DSi are region-locked, and cartridges released by iQue in China can only be played on DS models produced by iQue (although they remain compatible with other DS cartridges). The Nintendo 3DS line however, does enforce region locking for 3DS-specific software,1 with the exception of Nintendo 3DS Guide: Louvre, which is region-free."

As in Ryan's answer, Nintendo DS games aren't region locked. I can confirm this myself as I'm in the UK and I regularly import US/Japanese games that don't make it over here.

However, the Wiki quote raises this small caveat that I feel needs explaining more:

software specific to the Nintendo DSi are region-locked

What this means is that, if you use a DSi (and by extension, a DSi XL/XXL), any games/software that use DSi specific features become region locked. This is worth remembering because there are some popular games (Such as Pokémon Black/White and their sequels) that make minor use of these features and therefore become region locked on a DSi.

This only affects DSi consoles, however - they can still be played on the regular DS with no issues.