You can play electric guitar without an amp. In fact, it is better to practice without an amp because you can hear all your mistakes. Electric guitars are too quiet to play without some kind of aid. The best way to practice without an amplifier is to use headphones. With headphones, you simply put them on, and you can walk around playing your electric guitar anywhere you like.
Purchase a guitar headphone unit at your local guitar shop. Install a battery in the unit if it doesn't have one.
Put the strap on your guitar and stand up.
Clip the headphone unit onto your belt. Plug your guitar into the unit using the same cord that you use to plug your guitar into an amplifier.
Turn the volume control down on the unit. Turn the unit on, and gradually turn up the volume control on the unit.
Play the guitar normally. Use the volume and tone controls on your guitar as you would when plugged into an amp.
Some headphone boxes have all the effects of regular amplifiers, gain, reverb, tone controls and processors.
You can also purchase software that allows you to plug your guitar into your computer, and then plug headphones into your computer .