L293, L298 and SN754410 H-bridge drivers on low voltage power supply

For low voltages, it seems like the DRV8837 is pretty good: -

With an 800mA load, the volt drop is: -

\$I_O\cdot R_{OS(ON)}\$ = 800mA x 0.33 ohms = 0.264 volts. At this current, the power dissipation will be 0.8 x 0.8 x 0.33 watts = 211 mW.

Compare this with the L293 power dissipation at about 800mA - maybe about 3V is lost giving rise to a power dissipation of 2.4 watts.

The VNH5200AS-E from ST is also pretty good and is intended for supplies as low as 5.5V up to 18V: -

Also, another offering from ST is the VN5770AKP-E. It can be configured as separate top-side and low-side MOSFETs (including drivers) or just wired as a H bridge.

There is also the MC33887 from Freescale (formerly Motorola): -

It has on resistances in the low hundreds of milli ohms too.