TBH, people would never accept those with "powers". The reality of what would happen is what I really wanted the show Heroes to create, but they just assumed NOONE ever found out.
In reality:
Some power-people would start crime sprees, many people could be possibly killed
Those in the military found to have powers would be used in speacial operations
Some would be tested (not experimented/operated on) to determine the cause of powers
Children with powers might be taken into protective care
Parents might call for children with powers at their kid's school to be withdrawn, or withdraw their kids themselves
A new kind of power struggle would rise between nations with power-people
Some people would dress up like superheroes and try and do the things they do in comics
Some people would lynch "freaks" in their neighbourhood
There would be massive protests and campaigns across the world, for superhuman rights or superhuman discrimination/experimentation/euthination
That would be an incredibly intresting show...rather than the meh of Heroes