Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the butter, sugar, and brown sugar until smooth.
Beat in the eggs one at a time, then stir in the vanilla.
Combine the flour, baking soda, and salt; stir into the creamed mixture until just blended. Mix in the oats.
Drop by teaspoonfuls onto the prepared baking sheets. Flatten each cookie slightly with the back of the spoon.
Bake for 8 to 10 minutes in the preheated oven, until the edges are golden. Cool on baking sheets for a few minutes before transferring to wire racks to cool completely.