Square Platforming

The New Tetris, Square mode of Tetris Worlds, and Lockjaw: The Overdose reward the player for creating 4x4 block squares out of four tetrominoes. Building wide platforms (flat top sides) into the top of a square in progress allows more than one such square to be built at once, keeping options open for handling any tetromino.

Monosquares
It is best to use rotational symmetry (also called the "spiral" method or the "swastika" method) to make monosquares with platforms 3 blocks wide.

Spiral L monosquare, on both sides:

Spiral J monosquare, on both sides:

Spiral T monosquare, on both sides:

L on the left and J on the right require a double slide (see below).

Multisquares
SJSJ | ZLZL:

JSSJ | LZZL:

ZLTT | SJTT:

ZLLZ | SJJS (Gilly claims that this is possible, but it requires uncommon wall kicks to be present):

STTJ | ZTTL:

TZTJ | TSTL:

LTZT | JTST:

LTTI | JTTI:

LSIL | JZIJ (requires double slide):

Double slide
The New Tetris uses smooth falling animation for tetrominoes. The way this implementation mixes the falling animation with collision detection means that a tetromino can normally slide only one block under an overhang unless there is something on the floor to support it.