1. Active Person. You need to pick someone who is active and likes to exercise. If you pick a couch potato, you may find yourself consuming too much energy convincing them that it's time to exercise and not enough time making your workout better. Constantly begging your workout partner to get up and go can have a negative impact on your own drive to exercise.
2. Similar Fitness Level. Picking someone that is at a similar fitness level will help both of you stay motivated and on track. If you pick someone who is years ahead of you, they may push you too hard and too quick leaving you sore and wanting to quit. If you pick someone years behind you, you'll be doing all the "pulling" which can eventually wear you out.
3. Dedication. Make sure you pick someone that is dedicated, not necessarily in exercise, but in other areas of life. If you know this person quits every project they've ever started, why would exercising be any different to them?
4. Knowledge. Pick someone who has at least a basic understanding of exercising and working out. You'll be using each other to build your workout and incorporate new techniques. If the other person doesn't know anything about the topic, you'll never get any new ideas and keep doing the same workout each week. This isn't a recipe for reaching your fitness goals. Constant change and new ideas are needed to see long term improvements.
5. Personable. Maybe most importantly, make sure that you can spend a lot of time with the person you workout with. Do they easily annoy you or get on your nerves? If so, they aren't the best choice for you. Exercising takes about 60-90 minutes 3-4 times per week. If the person really likes to get under your skin, how motivated will you be to spend 4 hours or more per week with them?