I know you have to save either Ashley or Kaiden in Mass Effect but I'm not sure if they appear in 2 or 3. I'm just wondering, really.
Yes. If you import your previous save, then whichever one's life you save will appear in Mass Effect 2.
If they then survive Mass Effect 2, and you then import your save to Mass Effect 3, they will appear in that game as well.
They may be a romance option as well, depending on your character's sex and decisions.
This means you could potentially have a continuing romance with a single character throughout the whole series, making this one of the more significant choices in the series.
Do either of them appear in Mass Effect 2 and / or 3 depending on who you save in Mass Effect 1
The impact of either choice is felt through the franchise, in one way or another but that's true for most decision points in the series. Remember that the game is written in a way that nothing is ever free.
Assuming you will import your game save between chapters, the survivor will briefly appear on ME2 and will be a major NPC in ME3.