I often make a basil and garlic sauce. Put a couple of cloves of garlic in a mortar and pestle with a handful of basil plus some sea salt and mix until you get a paste, then add some extra virgin olive oil. I normally serve it with grilled chicken.
I usually turn my basil into a paste with olive oil and garlic, then freeze. From there it can go into most sauces or be turned into pesto. Pesto (or the more basic paste) can also be dolloped into the cooking liquid for rice. If your basil is just plain, you can use it in Thai and Vietnamese cooking as well. Especially great in green curry.