I played Runaway 2 first, and then Runaway I and in the end Runaway 3
While playing Runaway 2 I didn't know who some characters were, that appeared in the Runaway: A Road Adventure (like Joshua, Sushi etc) and it wasn't really explained in the game. After that I played the first game, and all the pieces were put together.
But since Runaway 2 finished with a cliffhanger, and I played the first game while waiting for Runaway 3 to come out, so by that time I have mostly forgotten the ending of Runaway 2, and couldn't remember what happened while playing Runaway 3
So I do recommend you to play the games that have sequels in order (unless they have totally separate and unconnected stories (e.g. Discworld Noir)), unless you want to get everything mixed up
