A full answer does require some feedback on what your goals are with lifting. However, regardless of your goals, proper technique for any lift is very important. What many people fail to realize is that many lifts require a fair amount of flexibility to perform correctly. If you cannot perform a lift correctly, your chance of injury goes up.
Let's start at the basics:
- You need the ability to perform the full range of motion (ROM) for the lifts in question. Squats require that your hips break parallel to strengthen the posterior chain and protect your knees. Several other lifts require full ROM to protect yourself from injury.
- Proper stretching helps you perform better with resistance training.
Now, with the basics taken care of we can address the issue of being too flexible.
- You need a stable platform, or base to perform many lifts such as pressing movements (bench press, military press, etc.). Any movement outside of what you are doing with the bar will affect your ability to perform the lift.
- Someone who is so flexible that they are prone to hyper-extending their joints will cause excess stress on those joints--particularly with heavy loads. Being strong helps, but you need to be extra careful when you push yourself.
Some people are afraid that stretching lengthens the muscles (which it does), and their goal is to look big. This is a short-sighted approach to lifting weights, even if aesthetics is your goal (i.e. bodybuilding). It's also a myth that seems to perpetuate in high-school gyms. Bottom line is you need the full range of motion to perform the lift properly and safely. Once you can perform the techniques correctly, you can push yourself harder to more than compensate for that little extra bulging that might come from tight muscles.
There is yet one more therapeutic aspect to stretching after you lift: it helps blood flow through the muscles better to repair them. Foam rolling is a godsend for lifter's aching muscles.