I just had this happen yesterday - drove through a serious downpour and the high humidity caused a lot of condensation to form. When I made a left turn I heard the HVAC blower fan making noises like it was getting hit with water; making right turns caused water to run onto the passenger footwell.
Turned out that my drain line wasn't clogged, but the was not pointed in the right direction. On my '04, there is a metal tube sticking out from the rubber grommet in the firewall and this metal tube had been turned so that it face slight upwards, instead of pointing down to the ground. This allowed the water level in the evaporator case to rise higher than normal, causing my problems.
So, first check to see if the tube is pointing straight down or nearly straight down before trying to clear the line.
2004 4WD Tacoma XtraCab 5-speed TRD
1991 4WD Jeep Cherokee Laredo 216,000 miles (owned since new)