Does the exhaust termination on a high efficiency furnace need to be at a 90 degree on the exterior of the house? I recently had both the intake and exhaust pipes replaced. The intake on the exterior is on a 90 degree angle pointing down, the exhaust pipe on the exterior has a straight termination - extending about 10-12 inches from the house. Should this exhaust be at a 90 degree angle pointing up?

I wouldn't point it up, you may get rain and debris in them. Many of the units I have seen, my house in particular, the two pipes exit straight and then have 45 degree ells set 90 degrees apart. Make sure to put small galvanized screens over the ends, I had a terrible time with hornets building a nest and blocking the intake.

I'm not a heating expert. I just know that people have died from high efficiency furnace flues releasing such cool air that it sinks back into the house, bring CO with it. I would guess that pointing up would not be good, since it takes warm air to rise.

The intake is pointing down using a 90 degree elbow. Do you think the exhaust pointing straight out - (extending a few inches beyond the intake) - is okay? Thanks!

Yes, it is just fine. However, it wouldn't hurt to look in the install instruction book and see exactly what it says for terminations. There are usually a variety of ways to terminate, but having the 90 down on the exhaust and the intake straight out will not create a problem, unless they are so close together that the intake is sucking in the exhaust.
Definatley do not turn a 90 upwards on either.

Put a 45 degree elbow on the exhaust and point it away from the intake. I wish I was more literate in putting in a design. Hope we have been helpful.