There are a lot of different ideas out there about lifting speeds. Some people tell you to lift slow, some say lift fast. Some particularly power-mad coaches will even try to prescribe the exact amount of time for the eccentric (lowering) and concentric (raising) portions of the lift, as well as the amount of time you should pause between each.
The slow rep or precisely timed methods might work for advanced bodybuilders who have decades of high-level training under their belts and who don't care how strong they are as long as you can see the definition in their pecs. For anyone other than a professional bodybuilder, there is one speed you should go: fast.
Why should you go fast? Power. Whip out your old high school physics book, and you'll find the following equation:
We can tell from this equation that the longer you take to perform a given task (the "work" part of the equation), the less power you are producing. So a lifter who takes 1 second to complete a rep of with 200 pounds is producing much more power than a lifter who takes 3 seconds to complete one rep with the same weight.
So it takes more power to lift faster. Using more power in your workout means you're building more power. Simple enough.
Why should I care about power, you ask? I'll tell you why. Power is basically the real-world application of strength. Pure strength is isometric, when you're exerting force but nothing is moving. Power is dynamic, when you're exerting force to accelerate or decelerate an object. So while pure strength might enable you to hold 300 pounds overhead, you'll need lots of power to move the weight from the floor to overhead.
There's another reason you should lift fast. Lifting weights at a certain speed builds strength at that speed AND ALL SLOWER SPEEDS. Train fast and you'll be able to lift heavier weights slow. Train slow, and you'll still be able to lift slow, but you won't be building power like you would lifting fast.
Now a bit of qualification: don't pick a super light weight and throw it around as fast as you can. You should lift fast, but controlled. Never lift so fast that you're in danger of throwing the weight away from you or your form breaks down. If you can go that fast, you're not using enough weight! You should lift like you're trying to throw the bar up in the air, but if you find that you're actually almost succeeding in doing so, add some weight to the bar.