Without a doubt, I'd pick cilantro. Like a squeeze of lemon or lime, its flavor brightens any dish and for me, there is really no substitute. Ironically, I lived for two years virtually cilantro-free on an island — Japan, where the taste of cilantro is almost universally hated. I wouldn't want to do it again.
Yes, I'd probably miss basil or parsley if I wanted to cook up a batch of pasta, or thyme if I wanted to make a French lentil salad, but I'd be even sadder if I had a plate of rice and chana masala without a healthy sprinkling of cilantro on top.
So what's your pick? Which fresh herb could you never live without?