I'm not from the US so I've no idea of the dimensions of the LED because I don't know the size of the coin in the picture.
I assume the bad didn't have a part number printed on it?
Where did get them from? A friend, ebay?
If so it's pot luck, they could be anything.
If you want to know the maximum forward current, test one to destruction. Build a constant current source, connect the LED to it, ramp up the voltage whilst measuring the voltage across it, until the LED gets too hot and smokes. The absolute maximum rating will probably be half the destructive current and the recommended forward current will be between half and three quarters of the maximum rating. Also look at the voltage across the LED and compare the voltage/current characteristic with a range of white LEDs, if the forward voltage of a standard white LED is 3.5V under the recommended forward current, the chances are you're safe running your LEDs at whatever current you measure when the voltage is 3.5V.
They look kinda similar to the CREE leds here
http://besthongkong.com/product_info.php?cPath=19_53&products_id=549
I've never bought from
www.bestofhonghong.com before, has anyone else? How can you be sure they sell genuine parts? I'd be wary of buying from some Chinese website, they might not be Cree LEDS, even if they're supposed to be.