I transport my bike in the back of my car (Prius) all the time. It could fit with both wheels on, but I find it easier to maneuver if I remove the front wheel. I put it fork-first with the drivetrain side up. Someone recently told me it would be easier to handle if I put the rear wheel in first, but I haven't tried that yet.

It you take either wheel off, make sure you remember to put everything in the car before you drive off. A friend once left her front wheel behind after removing it to put her bike inside the car. Fortunately it was still sitting where she left it when she went back to look for it. I always check around all sides of the car before closing the hatchback, just to make sure I haven't left anything on the ground.

Another thing I've learned is to avoid wearing light-colored clothing, especially pants, if I'm going to be getting the bike in and out of the car while wearing street clothes. It's easy to get your clothes dirty while handling the bike, especially while you're still getting used to lifting it in and out of the car.