Let's assume for a moment that any player that is not currently in the 8-man rotation that Karl uses will not be traded. This means the following players, no matter what, will not be traded:
Anthony Carter (due to Bird rights)
Keeping it (relatively) short:
Johan Petro (also has Bird rights?!) or Joey Graham for Nathan Jawai (Min). I have always liked Jawai and he is BIG. 6-10 and 280 pounds of beef. Would fit perfectly right alongside Nene, or in a big lineup (Melo-CB-Nene-Jawai-Martin). Salaries match straight up, he's young, and it's not like Minnesota doesn't have a surplus of bigs anyway.
Johan Petro or Joey Graham for DeAndre Jordan (LAC). DeAndre is another big body, slightly taller than Jawai at 6'11" but a little lighter at 250. He works the glass and is currently stuck behind Camby and Kaman, so I can't imagine he'd object to being traded to a contender.
Renaldo Balkman for Spencer Hawes or Jason Thompson (Sac). Not sure why Sac would do either of these, but Balkman is a capable PF and could fit alongside Tyreke and Omri pretty well. I mean, their only other PFs are Sean May (LOL) or Kenny Thomas, so it couldn't hurt to ask, right?
Renaldo Balkman for David Andersen (Rockets). Balkman rides the pine for another team. Again, no real benefit either way here, but David Andersen is 6'11" and 245, another player who could play a true C.
Renaldo Balkman for Hamed Haddadi (Memphis). Haddadi is never going to see PT behind Gasol, Randolph and Thabeet. He's a capable player and is 7-2 and 265lbs, a true seven footer who would actually see time in the lineup.
That's about all I could dig up now, but all of these trades work in the trade machine, all are to teams who might be receptive, and with the right filler (cash, picks, etc.) could all work, WITHOUT giving up any of the core Nuggets rotation as it stands.