1. No Name Lake and Bend Glacier via Broken Top Trail – considered one of the best hikes in the state.
2. Tamanawas Falls – Mt Hood
3. Tom, Dick, and Harry – Mt Hood
4. Hamilton Mountain Trail – Gorge
5. Maxwell Lake – Wallowas
6. God’s Thumb via The Knoll – Oregon coast near Lincoln City
7. Clatsop Loop Trail – Ecola Park – easy but good views. Great intro trail.
8. John Dellenback Dunes Trail – Oregon coast near Reedsport
9. Natural Bridges Viewpoint Trail – South Oregon Coast – probably most amazing views of multiple natural rock bridges and coastal rock formations.
10. Trail of Ten Falls – Silver Creek State Park
11. Misery Ridge Hike – Central Oregon
12. Tumalo Falls Trail – Bend
13. Green Lakes/Soda Creek trail – Bend –
14. Cleetwood Cove Trail – from rim to water at Crater Lake

Major multi-day hikes:

1. Three Sister’s Loop – 46 miles
2. Steens Mountain Gorges Loop – 28 miles
3. Paulina Peak trail – gorgeous sunrises, rent a snowmobile in winter
4. South Sister Trail to summit – 12 miles

More information and some of them taken from here.