Olive green is a slightly yellowish green, usually characterised by a bit of a neutral shade. Neutral shades, those in the range of grey or browns, are a mix of all colours. Since olive green is somewhat tempered by its neutral component, it is easier to pair with other colours than brighter shades of green. Whether you are looking for a match for a room, a painting or for a hobby project, you have many options.
Yellow and yellow-green
Yellow is next to green on the colour wheel, and goes with it very well. A bright yellow such as canary yellow will be a lively counterpart. Pastel yellow will work, too, letting the darker olive green take precedence. Gold is another option to consider, especially a metallic gold or bronze colour. Yellow-greens also are options, with the brighter versions adding verve and snap.
Earth tones provide a solid pairing for olive green. They are not so colourful in themselves, but would give a solid base from which the olive green would stand out. Classic lighter colours such as taupe or tan are in this family. You could also use deeper earth tones like umber for contrast.
Red is the complement of green. As such, it will set up a dynamic contrast for the olive green. Vermilion, a brilliant red, would make a rich companion. Jewel colours such as garnet or ruby could also be successfully employed. For a softer red where the olive green stands out more, an autumn colour like russet will do the job.