If the equipment you are using does not have a ground plug, it does not matter if you have a grounded adapter or not.

I say if your stuff is two prong, you only need a two prong adapter, and it will work everywhere.

If it's three prong, to keep the ground you will want a three prong adapter, and should you come across an outlet that is only two prong, it won't work, but those are probably rare. The best solution is probably to have both.