Ok... I was playing a casual game with my Green-Blue deck (mostly green, I have like five cards that need blue mana in the whole deck and a couple of islands for those cards), and my opponent played {Nightveil Specter}. I was getting pretty mana shafted and was drawing all high cards; so I couldn't block the card for a couple turns. I ended up having to exile a {Forest}. If I remember correctly, once a card is exiled no versions of that card are allowed in play; so all of my {Forest} cards are now in exile. Is that the way it really works? Can {Nightveil Specter} exile basic lands? If so, that card is too over powered. It would be murder to play a mono-colored deck against any deck containing that card.
I'm not too sure where you get that impression from, but exile only meant that particular card is taken out of the "playable" zones and is usually not able to be used unless a card says so, in this case I believe your opponent can play the forest he exiled from your library.
And you can continue to play your other copies of an exiled card so long you followed the rules of course.
Only that particular card is exiled. And they can play it, yet they can still only play 1 land per turn.
Ok... I think the idea came from a friend's misinterpretation of a card that said something about exiling every version of a card when my husband played casually, and we've just always played that way...
Felt like {Detention Sphere}.
You may have just been thinking of cards like {Slaughter Games} or {Surgical Extraction}. These cards are special exceptions, and note that it says to do the extra removing of copies of the cards specifically. Normal exile is, as everyone above says, only going to remove the card being exiled.