Standard USB ports only deliver max 500mA of current, and then only after negotiation with the connected device, which Raspi doesn't do, while Raspi requires 700mA. Lately some computers have come out with special "charging" ports that can deliver more current, intended to charge mobile phones and tablets, and it should be safe to power the Raspi from one of those. What will happen if you connect a Raspi to a standard USB port anyway? That depends on the design of the USB host (computer). If the port is protected by a polyfuse of the same kind as used in the Raspi itself, it will likely start to boot up fine, possibly even finish booting, but then die. Disconnecting and waiting a few minutes will reset the polyfuse and allow you to use the port again. Of course, you may also get away with running the Raspi this way with no problems, either because the Raspi isn't drawing the full 700mA (depends on what you have connected to it and what you are using it for), or the designers of the host allowed for more than 500mA current, or the USB port has ineffective overcurrent protection (cheap USB hubs may, indeed, have no overcurrent protection for individual ports).
Best regards, Kári.