is fat free pudding healthy?

It's OK to have it once in a while. Though calories aren't nearly the worry in nutrition. You also should be very aware of the contents of what you eat. Pudding, as any other manufactured food, has many things to make it stable, last longer, and look good. But in reality they add many preservatives and food colorings for its beauty and taste. You should also be aware that pudding includes animal fat for gelanitisation and gel texture, and 99% of the time this animal fat is pork because it's the cheapest, so beware if you don't eat pork.

Other than these issues, in general i guess there's no harm in pleasing your taste buds :)

PS: beware also, that in the "light" or "fat-free" etc, they often add some sugar substitutes to avoid high calories but in reality most of artificial sweeteners have found to be carcinogens (cause cancer) in a long period of time.

It depends on what you mean. It is low calorie and a better choice than say, full fat ice cream. Would it be better and just as nutritious to have, say skim milk -- yes. I also find that the pudding mixes have a lot of sodium. But in general, a tasty treat and good alternative to high cal, high fat deserts.

"healthy" is such a subjective word. heathier than regular pudding, maybe...but healthy in general...no.

Tastes horrible too. Eat an apple.