1996 Accord EX AUTO, lately my brake pedal has felt mushy. Soetime when I am completely stoped the brake starts to travel down slowly and I have to press it all the way down so the car doesn't move. IF I pump it a few times it starts to work normally.

 

Perhaps you have gotten some air in your brake lines. I would suggest getting a new bottle of brake fluid, then bleeding your brakes. Consult the corresponding Haynes manual for your model car and follow the directions. It really takes two people to do it right.

Another alternative is that you have really worn the pads down on your car and are having to stomp even harder to depress what's left of them into stopping the disc/drum.

 

either
a) air in the brake lines
b) low brake fluid
c) failed master cylinder

the master cylinder failed in my accord after 70kmi. but i drove that thing pretty hard :P

 

You could also have a small leak in one of the lines and pumping up the pedal is giving you more vacumm to help boost pedal feel.

 

just bleed the brake lines.