I tried grilling some peaches to go along with a new pork tenderloin dish I was trying out and I found that adding some shreds of basil really enhanced the overall taste. Get creative and experiment. If you love the taste of basil, like I do, you can do no harm.
Basil plants are annuals, so they are only supposed to last one growing season. Don't be sad when your basil plant doesn't last forever; they are inexpensive and you can go get a new one. This plant was only $5 at the Union Square farmers market. They like sunny windows, water every other day or so, and be sure to pinch off the big leaves so the little ones can grow. Once the basil plant flowers it will probably stop producing new leaves, (this is the end of it's growing period) but if you trim off the flowers, you may be able to trick it into producing leaves a little bit longer. Go get one and start cooking!