theres no amp rating on the bread board but i get what giftiger_wunsch says "It's a bit like asking the max current for a wire: i'd imagine it varies"
but i found this 6v 300mA plug in down in my basment and its perfect
it puts out 9-10v wich was what i was aiming for... i attached small alligator clips to the ends and whalaa it works great and now i have 6 extra 9v durecell batterys i wont be using as much anymore
I did some testing on a breadboard for a little SMPS some years back, the breadboard connectors were getting significant heat losses (which I measured as resistive losses) when over 600mA, this was worse with thin wires plugged in like standard (thin) resistor legs and not as bad with larger wires plugged in due to the much higher clamp force with larger legs.
This was with a new good condition breadboard and I had amp and voltmeters all over it to test the efficiency with changes in component values and it was obvious the breadboard was becoming a liability anytime over 500mA.
I would not run a breadboard at 500mA or above for any length of time. And if the breadboard has seen abuse like large wires or worse still header pins stuffed in it the connections can fail at much lower current levels.
I haven't done any experiments but always assumed it to be about 1.5A. Now I know it's only 500mA I'll think twice before trying to push 1.5A through it.