With the Volt I will sometimes have gas anxiety, but only of it is close, like I am 7 miles frome home and range says 7 miles remaining, I will lighten up on acceleration, etc. Once only to be annoyed by the engine starting as I pulled onto my street.
I won't go out of my way to avoid burning gas, but I might plug in at work to avoid it if I can (with permission of course).
If I do have the engine start I drive it until it is warm (winter). Usually I know this will happen and put it in mountain mode with a few miles range remaining and get it nice and toasty before finishing the trip on electric.