Can I connect ground to neutral in a 3 wire outlet?
Bridging the neutral and ground at the outlet is against code. This is called a Bootleg ground. You have a few different options to bring this up to code (corresponding to the NEC electrical code):


Replace the outlet with a GFCI outlet, and leave the outlet's ground unconnected. This is minimally dangerous, the risk is if you get your body somewhere in between the hot and neutral.... but it'll protect you if current tries to flow between the outlet, and devices on another outlet (or the ground).
Add an additional ground wire. The wire must be of the proper gauge, and go to a "grounding electrode", or your main circuit panel. There are a few other details that you'd need to follow. See NEC 250.130(C) for details.
Rerun the wiring for the outlet with three-conductor cable/conduit.
Replace the outlet with a 2-prong outlet.


Keep in mind that the ground and neutral should be connected together at your house's service entrance, and nowhere else.

The "ground" connector is often connected to the chassis of electric equipment, for example the metal case of your oven, lamp, etc.... One danger is that the neutral is not really at the same potential as the ground. The neutral wiring from your device has some non-zero resistance. The electric current flowing through your device also flows through the neutral wire. The current flowing through your neutral causes the voltage of the neutral to increase (based on Ohm's law, voltage = current * resistance), which can cause your neutral to be a few volts above ground. So, if you have a properly grounded device, next to a device connected to your bootlegged ground, you can shock yourself by touching the two cases since they will be at different potentials.

A second problem with connecting the ground to the neutral happens if your neutral wire breaks between the outlet and your service entrance. If the neutral breaks, then plugged in devices will cause the neutral to approach the "hot" voltage. Given a ground to neutral connection, this will cause the chassis of your device to be at the "hot" voltage, which is very dangerous.