It depends. Some wineries provide complimentary tastings of their various wines. Other wineries may ask you to pay a dollar or two to sample their wines. If the winery is tasting a special or reserve wine, the fee may be upwards of $10-20 per person.
During the Thanksgiving Weekend, many wineries host special tasting events. These cost from between $5 and $10 per person, allow you to sample a wide array of special and reserve wines, include complimentary food and cheese to accompany your tasting, and also allow you to keep your tasting glass.
Before visiting a winery, you can call ahead and inquire if there is a tasting fee. However, for the experience of sampling fine wines, talking with the tasting room staff, and enjoying a wonderful afternoon at an Oregon winery, the tasting fee is probably minimal.