Well yes and no. It takes bandwidth to carry information, the more information you want to send per second, the wider the band of frequencies you have to transmit.
But there is no theoretical limit to the range of frequencies you can use. You could in theory send out a signal that went from 10KC to gamma rays.
Practically, it's hard to make a transmitter with a wide bandwidth. Usually 10% is considered wide, so if you're sending microwaves, say one billion cycles per second, it's hard to send a signal wider than 100 million cycles per second.That signal nowadays can encode about x times that number of bits per second, x is determined by the cleverness of the modulation scheme, and can range from 1/2 to around 4.
As for actually, in the laboratory they've sent around 300 billion bits per second over carefully made fibers. Using VERY fancy and expensive transmitters and receivers. Your typical fiber runs at under 1% of that speed.
