When you do long duration cardio (e.g. 2 mile run) you put your body into a catabolic state, or a "breaking down muscle" state. To build strength and muscle, you want to be in an anabolic state, or a "muscle building" state. Your body releases specific hormones under each condition. If you run a few miles right before you lift, you are gonna kill your performance in the weight room because you will have the wrong hormones (e.g. cortisol vs. testosterone) flowing and your body will be in the wrong condition for what you are trying to do. Another major reason is the fact that you will use up most if not all of your energy stores (glycogen) before you ever step foot into the weight room. Yet another thing to look at is the fact that activity like distance running primarily recruits slow twitch motor units and muscle fibers whereas activity such as lifting or sprinting uses fast twitch motor units and muscle fibers a lot more. This will confuse your body and hurt your performance also.
Taking these things into consideration, if you want to get stronger and build muscle, why in the world would you want to kill your performance by going for a run before you lift? If you are an endurance athlete who runs long distances in competition, then your main focus is obviously going to be on the long duration activity. However, even then you still need to get some effective strength training in to keep your body strong and prevent injuries.
The best way to do things is to do long duration cardio on a separate day or at a separate time so the conflicts betwen the differing demands don't hurt you, and if your main goal is to get stronger and build muscle, you shouldn't do too much of it anyway as it can have negative effects on your weight room performance. An even better way to go is to get your lift in and then finish up with some intense conditioning such as sled dragging, circuits, sprints, etc. as these forms of cardiovascular work help performance and fat loss better than long duration, boring cardio anyway(see earlier posts or articles section for more on this).
In conclusion, lift first and finish with some intense conditioning; perform long duration aerobic work at a separate time. If you must do them both around the same time, lift before you run, bike, etc. as lifting won't hurt the others as much as they will hurt lifting.
If anybody has any thoughts on the topic, I would love to hear them.