I replaced the brake light bulb on Toyota Camry 2005 but the lights still don't work. Any idea as to what else to check and how. Thanks in advance.

. Test all under dash and under hood fuses with a test light or multimeter.

. Test/replace brake light switch. Before replacing, spray with WD-40.

. Check brake light switch adjustment.

. Check for socket corrosion.

. Check for hidden broken wire, such as around the driver's side trunk hinge. Opening and closing trunk can cause an internal break in the wire, over time. May need to cut open the bundle wire covering and probe each wire for continuity.

Excellent advice above, as usual, If you have a meter, you could check for voltage to the brake switch, if so, jumper/bypass the switch with a paper clip or wire.
Can you put into gear?

Are both side brake lights not working or just this one side?

I like your advice but I have an opposite problem... Cyclops and brake lights stay on even after car is turned off. Cyclops even started to melt red cover... I'm no mechanic but can diddle. I've replaced all obvious bad bulbs and still can't fix the problem... The flashers make that fast sound of something wrong but I can't even locate the flasher ( man I miss VW's). Also the two front fog lights don't work. One may be burned out... Is this one of those situations that one little bulb can make everything malfunction or am I just getting old?? Thanks for any advice... Terry

Unplug the brake switch on brake arm, if brake light goes out, the brake switch needs to be replaced or adjusted.
As far as the flasher, In the old days, if a bulb was out, it would flash slow, newer cars flash fast when a bulb is blown?
Can help more after you unplug brake switch.

Adamstw, see if the brake pedal pad is missing. If there's a hole opposite the brake light switch in the brake pedal, the brake pedal pad has deteriorated and fallen out. It's the size of a LifeSavor and just snaps in. If it's missing, the brake lights will stay on and drain the battery.