The level of the 3D effect really depends on the game. Pilotwings and Street Fighter really seem to stand out big time, same with Steel Diver and Nintendogs (at the right moments). Also depends on your individual vision. Some people with great eyesight still might not see it as well as someone with medium to bad vision. I'm not entirely sure how it works, but I can see the depth perception quite well.
3D in general doesn't add to gameplay, but for some games, it does make certain tasks a little bit easier to not screw up (such as flying through rings, hitting a block within a 3-Dimensional world, and judging the proper distance between two cars), so in a way, it adds to the enjoyment of already established gameplay.
Take Metroid: Other M for example. In that game, sometimes its really hard to judge what's an actual platform, as opposed to just the background itself. 3D in a game like that could really help when you're jumping around. So again, it doesn't technically add to gameplay, but it definitely makes certain annoying gameplay elements drastically more enjoyable and easier.
