What is the maximum charging current of the MAX1737?
The MAX1737 uses external MOSFETs for charging output. It is essentially a controller chip. Therefore the result depends on transistors (and magnetics).

EDIT 1: The limitation in marketing materials is likely because the controller can't drive more powerful MOSFETs efficiently, and 4-A was a practical limit. Power MOSFETs can have 10 nF gate capacitance, and with 7-Ohm driver inside the MAX1737 the turn-on transients can be 100-200 ns, which, at 300 kHz operations (pulses can be sub-1-us in some regimes of charging) would lead to likely unacceptable losses and transistor overheating. See Section "Application Information", MOSFET selection. The fast charge current, however, is not limited by any particular restrictions on the value of set resistor, it can be anything.