It depends on what line you'd like to emphasize. The cabinets line, or the countertop line... Also would depend on the configuration - how far beyond the cabinets does it extend? Personally, I think it's more natural to stop with the cabinets....

If you have a nice border for the backsplash you can extend it all the way with the counter, if you're running the tile up to the cabinets and not using any borders you can stop with the cabinets and leave a short piece of the counter without the backsplash. If there's a large difference between where the cabinets end and the counter ends, then it may look better to take the backsplash all the way with the counter.

If you stop at the cabinet line, how do you finish the countertop area that has no backsplash above it? Also, was wondering how it would look to extend the backsplash all the way out to the door opening which would be about 2" beyond the countertop?

We ran our backsplash beyond our cabinets and out to the end of the counter, with bull-nose edge and corner pieces to finish the edges on the side and top wall areas where there are no cabinets for the tiles to run into. It all looks very finished.

It would be a great help to see a picture. There are so many different ways of doing this.

Here's a quick picture of two examples, one where it ended with the counter and one where it didn't.