People above have mentioned great flies. Some killer knowledge to have is what insects are hatching at the time. You can find hatch charts for many local rivers on the net. There's a few here:
http://stoneflysociety.org/hatchcharts.htm
Once you know what's hatching you can fish with flies to match those insects. For instance Pale Morning Duns (PMD) will be starting soon. These are mayflies in a light yellow color. This hatch usually starts in the afternoon. Having flies that imitate the whole life cycle of a mayfly will give you an advantage. Hours before the hatch starts you can start fishing a PMD nymph. The nymphs will swim up the water column and you can start fishing an emerger right below the surface. Once you see fishing rising and see the adults on the water it's dry fly time. So just have flies ready for all the possible bugs and you'll be set! Size wise, most of my flies are 16-20, some bigger some smaller.
Here's some killer flies:
Sow bug, Pheasant tail, Hares Ear, Copper Johns, Wd-40, RS2, Rainbow Warrior, Prince, San Juan Worms, Hares Ear Soft Hackle, BWO/PMD soft hackle, Zebra, Barr's Emerger, Parachute Adams, BWO thorax, PMD thorax, Stimulator (awesome on the upper), Elk Hair Caddis, Assorted Ants and Hoppers, etc.
Having those in varying sizes and BH versions will give you a great start! You can never have to many flies.
^^ike
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