Some days, people just don't have as much time to spend in the gym as they wish they did. The still want to get in a great workout, but they have to do it in less time. It is entirely possible to get a high quality workout in less time. However, you have to be willing to move quickly and take less rest time between sets. Here's how a typical quick upper body routine might work. The types of exercises that each person uses may vary, but the speed and the alternation should remain.

Chest
Perform two chest exercises. First, do a single set of flat bench dumbbell presses with your typical starting weight. As soon as you finish the set of presses, begin a set of flat bench flies. After finishing the two sets, rest. Repeat this process two more times, but keep the weight the same. Finish off with a set of pushups to failure.
Triceps
Because the chest and triceps work together, move into the triceps next. Do a set of straight bar press downs with your typical starting weight. After the first set, immediately reverse your grip and perform reverse press downs. Rest and add weight. Repeat the process two more times.
Shoulders
Begin with upright rows with dumbbells. Perform a set and then move to a lighter weight for lateral arm raises. Rest, keep the weight the same, and repeat twice more.
Back
Pull downs on the lat machine are the first order of business. Do all three sets with limited rest in between. Move to the rowing machine and do three sets with little rest between.
Abs
If you are making good time on the workout, you can do your abs at the gym. Some crunches and leg lefts will help to finish of a fast upper body workout. However, if you are hurting for time, consider adding the abs when you get home. You don't have to have much room at home to do them, and you don't need to have any special equipment.
Eliminate Your Long Rest between Sets
How long do you normally rest between each set? Some people will rest for well over a minute, and this isn't doing them any favors. You want to hit the muscle quickly, so you should lower the amount of time that you rest between each set. On a normal day, you can rest from 30 to 45 seconds. When you are trying to get through a quick workout, you should cut the rest time in half. This will increase your heart rate, which can be a good thing even when you're working with weights.
If the gym isn't overly crowded and you stick to the lower amount of rest between sets, you can cruise through a workout like the one above in about half an hour. If you notice that the gym is busy, consider eliminating some of the exercises and simply adding extra sets to the exercises and machines that are within range and open.