Hi gundamv--an opening which stays cramped forever is not a good one of course, so you're probably looking for a slower, more modern system that lets the opponent grab extra space in the center. Openings with such reputation include the French; after 1. e4 e6 2. d4 d5 3. e5, white already stakes a larger claim of the middle. Philidor's Defense is another one, with 1. e4 e5 2. Nf3 d6 giving black less hold on the 4th/5th rank than 2...Nc6 would. The Hedgehog is by definition a setup where pieces and pawns stay back until an eventual break with ...c5; common setups include pawns on a6/b6/d6/e6, knights on d7/f6, bishops on b7/e7, and queen on c7. Generally speaking, look for openings where the opponent is allowed to play both e4 and d4 (or e5 and d5) without much resistance. Some are outright bad, but the better ones will relinquish that space and effectively fight back for it later.
Looking for a cramped opening

^ Yes, what I am looking for is a slower system that lets the opponent grab extra space in the center. Thanks for giving me additional openings to consider.
Would the KID be considered "cramped," as I have described that term, given that White is usually allowed to play both e4 and d4?

maybe the czech/closed benoni.
black doesnt give up the centre but he doesnt have much room to move and usually maes some crazy knight journeys Nf6-Ne8-g6-Ng7 to play f5 and free himself a little bit.
Personally i quite like it, since black has a ready made plan, and most white players will probably be a bit less familiar with what to do.
The KID is a hypermodern system which purposely delays direct control of the center. Black inevitably strikes back using d6/e5 or d6/c5 within a few moves though; if he doesn't, he gets overwhelmed. So I'd call it unbalanced more than cramped, similar to the opposite-side attacking of a system like the Dragon Sicilian.

gundamv, A pair of defenses for you to consider are the French and Semi-Slav. The French is the original cramped defense. The Semi-Slav Moscow variation is cramped also. If you get to play the Meran, revel in the space you gain. Alexei Dreev is a practitioner of this repertoire.
#acrobatics

The Dutch Stonewall is a very cramped opening (maybe the most cramped of all?). It can be played as either black, or in reversed form as white ("Stonewall Attack"). Some people use it as a universal system for both colors. Playing it as white supposedly offers only equality, but afficianados of this system seem to do well with it (presumably because it takes subtle long-term thinking to play against it successfully).

Good question since 1.e4 is the one white move that most discourages black from playing the Dutch Stonewall (by discouraging the immediate 1...f5). Black might still be able to transpose to it by playing ...f5 later.
Against 1.e4, you might try the Philidor Defense, Czech Defense, French Defense or a hybrid of these (this is how I play against 1.e4 -- see my recent slow games). For example 1.e4 d6 2.d4 Nf6 3.Nc3 c6 4.Nf3 Bg4 5.Be2 e6 6.h3 Bxf3 7.Bxf3 d5, and black has disposed of his bad LSB and ended up with an improved version of the French Defense. Of course there are other independent variations depending on white's early moves. A recent book by Cyrus Lakadawal gives a good description of this system (click here to go to the amazon website and have a free look inside the book).

Nimzo-Larsen as white, Pirc and King's Indian as black. Much theory involves punching out of the cramp.

I think he just wanted an opening that was cramped to practice handling cramped positions, just as I used the Latvian Gambit as practice on how to handle positions where my king is exposed - not to use in a tournament setting. He could do King's Indian Defense/Attack for both sides using e6/e3 for practice.
I read somewhere that to improve, you should work on positions that are challenging for you.
I find that I do not like to play cramped positions because of the lack of piece activity. I am therefore looking for a cramped opening to read a few games in and perhaps play some games in, just to get a feel for ways to handle cramped positions.
One candidate, based on my prior experience with various openings, is the King's Indian. Is that cramped enough or are there better ones out there?
Lastly, please note that I am not changing my repertoire nor am I trying to learn the opening. I just want to see some common middlegame themes in cramped positions. So, considerations such as how theoretical an opening is or how sound it is doesn't matter as much, though I would prefer to look at games from a more commonly played opening than from an obscure opening.
Thanks.