This is a wide-open question. You can use lemongrass with just about anything and it will give your dish an Asian feel. Many pair it with beef, chicken or pork, and it is also very prominent in Asian soups. I think you mainly see it more specifically in Thai and Vietnamese cooking, but I'm sure there are plenty of other cuisines that also call for it.

Here are a couple great recipes:
http://food52.com/recipes/19077-mussels-in-a-yellow-tomato-lemongrass-broth
http://food52.com/recipes/19215-lemongrass-ginger-patties