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This list is an attempt to come up with different aspects to the rules of
chess that could produce an unlimited (unbounded) number of variants based
upon changing the parameters around this rule type.  Please suggest more if
you can, or critique.  I will look to update this as time goes on. 

I see this so far:
1. Board size and shape.  A board can theoretically be infinite in size. 
Because of this, it can theoretically take on an infinite number of shapes
(shapes representing the number of spaces it has, and where they are
located).
2. The number of players (and also number of teams).
3. Time control: Amount of time each player has to play.
4. Play to points in a chess tournament: Players can play to an infinite
number of points.

Probably unbounded (no sure):
* Turn order and sequence of play.  This is based off the way progression
works.  There may be a limit to how many times a player can move in a row,
given a minimum number of pieces, which the victory conditions can always
be met.  In light of this, this may not be infinite.

Some that I am uncertain about:
* The number of unique pieces.  Is there an infinite number of ways a
piece can act on a chessboard?
* Number of pieces on a board and their mix.  If a board is finite size,
then this should mean there can only be so many piece combinations on a
board, right?
* Reserve pool mix.  It is theoretically possible that you can have an
infinitely large reserve of pieces that can be dropped in from every turn,
but I would argue there is the possibility for a board to get clogged up
with so many pieces, that it isn't infinite.  Even shuffling the reserve
doesn't resolve.
* Adding new rule types.  Are there really an unlimited number of
different rule types that can be added to chess, that make it unlimited.

What I don't see as unlimited:
* Shuffles. Unless you have a theoretical unlimited number of pieces on an
infinitely wide board, it doesn't look infinite to me.
* Piece names and look. This doesn't functionally change how a game is
played.
* Board colors. Unless the rules governing pieces is governed by color of
the board, this is irrelevant to how the game is played.
* Space shape.  I would argue there is only a finite number of ways that
spaces can be fit together that they would fit together.  Now, the
combination of these pieces definitely could potentially fit under the
unlimited category.

Please reply with others and comment.  You can also go to the Chess of
Tomorrow Project Thread to discuss this more there:
http://chessvariants.wikidot.com/forum/t-51667/chess-of-tomorrow-project-who-is-interested#post-140383