Green is a pretty universally "friendly" color, capable of playing well with many colors across the spectrum. For example, green works great with other shades of green, blues, purples, yellows, and even oranges. It is recommended, however, that you avoid reds unless you are specifically going for a "Christmassy" feel.
If you're going for an accent color to work with green, you need to think about the over-all effect of what you are trying to achieve. Oranges work well for a high-impact color that stands out of the crowd. Blues will work well to keep the scheme looking uniform, but adding enough variety to make it look interesting. Yellow added to a muted green scheme can help add a bit of sunshine to make it seem less sleepy.
Green as an accent color:
Green typically adds a refreshing high note to most color schemes, helping to bring a high-energy feel into an otherwise calm, relaxed scheme. In lighter color schemes like with yellows and pale blues, green can add a soft, tranquil note to something otherwise almost overpoweringly bright.