As someone who has cooked with exactly one kind of mushroom (button) I find this intriguing. I thought all mushrooms taste more or less the same. I may have eaten something at a restaurant, but don't remember anything unique.
In particular, three of the most common western supermarket mushrooms (button, cremini, and portobello) are actually all the same species (Agaricus bisporus). They just look different.
Shiitakes are a different species and do taste different, but are somewhat related; at one point in the past they were classified in the agaricus genus.
Once you venture outside those, tastes and textures rapidly diverge. Truffles and morels are definitely memorable if you've never had them before.
My personal favourite is Chanterelle. Yellowfoot is pretty great too.
The strongest ones I would say are morel and of course truffles which are used for finest (and most expensive) delicacies, but many others which are more common are great too.
Huge huge differences in mushrooms.
My favs are chanterelles, chicken of the woods, and candy caps (which have a distinct maple/sotolon flavor).