As per the title. It can be due to unique gameplay elements, graphical style, storytelling methods, atmosphere, control style, humour, use of sound, etc. Anything.
Can also be "unique to a series", in which case you should mention the game in the series that provides the best example, or does it best.
There are plenty, but the first one I'll mention the Jet Set (Grind to the Americans) Radio series. I've personally only played Jet Set Radio Future (Xbox) but I loved it and it's a shame that there have been no sequels since. These were games about graffitiing (if that's how I spell that) a city, grinding on everything you could find on your roller blades, and pulling off crazy tricks in the process. Its own brand of fast-paced gameplay and a great looking cel-shaded art style made JSRF a truly unique experience for me.
What have you got?
Captcha agrees that this game is "the bee's knees".
Can also be "unique to a series", in which case you should mention the game in the series that provides the best example, or does it best.
There are plenty, but the first one I'll mention the Jet Set (Grind to the Americans) Radio series. I've personally only played Jet Set Radio Future (Xbox) but I loved it and it's a shame that there have been no sequels since. These were games about graffitiing (if that's how I spell that) a city, grinding on everything you could find on your roller blades, and pulling off crazy tricks in the process. Its own brand of fast-paced gameplay and a great looking cel-shaded art style made JSRF a truly unique experience for me.

What have you got?
Captcha agrees that this game is "the bee's knees".