Taxlady, Some things I have used Thai basil for are things that would normally use tarragon. I actually like the flavor better in most things than tarragon, which has an anise flavor, as well, but not as complex. An omelette de fines herbes is one thing in which I often substitute it for the tarragon. Most of the Thai dishes using Thai basil that I make do have a lot of unusual ingredients in them, though most of them take less time than it takes for the rice to cook.
Thai and regular basil are the herbs that made me start growing in hydroponics, so that I could have them fresh, 365 days a year!