This beautiful state has a lot of different rivers for you to enjoy. Most of the larger rivers will also have a decent population of salmon and steelhead in the spring, fall and winter. Some of the wilderness areas here are breathtaking with cedars, fir trees and large ponderosa pines, you can taste the humidity in the air and you feel like you can expect a bigfoot to pop out of the woods at any moment. I have not listed too many rivers here, but the state is literally full of them. I am careful about posting information on smaller less popular rivers. You can rest assured that driving in the mountains will lead you to plenty of small streams in Oregon that are filled with trout.
USGS current stream flow Data here
You can find the regulations and season information here at the Oregon Fish and Game website
You should also consider visiting this great site: Oregonflyfishingblog.com it is filled with great info and deals on gear.
You can find brooks, browns and rainbows in the upper sections of this river and steelhead throughout during the season. This river gets low in the summer due to water usage for irrigation. You can possible hook fish here during the winter, but there are better places to try on the main river.
This river has one of the best summer steelhead runs available. You can also catch spring steelhead in this area usually starting in January.
You can find great steelhead and salmon in the Nehalem river and bay. The North fork of the Nehalem is one of very few areas in Oregon that has a coho salmon season. You can also catch sea run cutthroat in this river system.
This river is very close to the Idaho border and is quite a ways from any heavily populated areas of Oregon. The area marked on the map (below Owyhee dam) is known as a great tailwater fishery. Lots of rainbows and brown trout can be found here.
The Metolius is a spring fed river starting in the cascades. It flows through a dense forest of pondersa pines and cedars. This is a stunning area to fish. The Metolius is open year round for flyfisherman and has special barbless hook requirements.