The real advantage to a manual over an automatic, like a couple others have said, is control. If you're cruising on the interstate and come up behind someone that you want to pass, if you're driving an automatic and you stomp the gas, you have a huge delay, first a delay before it shifts down one gear, and then another delay as it tries to shift down to a even lower gear. In a manual, you just shift straight from 5th (or 6th) down to 3rd and you're instantly in the sweet spot of the torque curve. Or, rev the engine up to it's peak torque rpm, drop the clutch, and you experience much quicker acceleration than any automatic can deliver.
You'll (almost) never find an automatic equipped car that is quicker than a manual, if the driver is any good.
As for paddle shifters, the only ones that will be quicker than most people shifting will be those from Ferrari or BMW (SMG). All other "sport" shifters are basically automatics that you give you an option of forcing gear changes, but you still have a significant (still tenths of a second, but they feel like eternity while driving) delay as the automatic changes gears, and you can't skip gears, either, so that makes it that much slower, too. I had a car with "Sportronic" shifting, and it's fun if you aren't used to a manual, but it won't deliver as many smiles as a manual will.
Ferrari and BMW make manual transmission cars that shift like automatics, they don't have a conventional clutch, instead have multiple clutches without a clutch pedal, and the paddles electrically actuate hydraulics to shift gears. The computer shifts the gear almost as quick as your brain tells your finger to tell it to shift, like .15 seconds, where the fastest humans can shift in about half a second, huge advantage in drag racing.
Check out this website:
http://auto.howstuffworks.com/dual-c...ansmission.htm