The higher-pitched, digital tone of an electric guitar makes it perfect for playing rock, metal or electric jazz. However, when you try to play acoustic songs, or music written for an acoustic guitar, it just sounds off. No matter how great your playing is, the sound from an electric guitar with a standard configuration will never match that of even a budget acoustic guitar. While you should never expect to get a completely perfect sound from your electric, you can maximize it's potential with some adjustments and accessories.
Switch your electric guitar strings to a heavier gauge. Never put actual acoustic strings on an electric guitar, but a heavier string will give a less electric tone when strummed. Strings from a brand name will also offer more tone than budget strings. On the downside, you will have to sacrifice the string flexibility and ease of use that light strings offer.
Adjust your guitar and amp settings. First, the pickup selector on a Stratocaster-style guitar should be set to the middle and neck combination position. On a Gibson-style guitar, set the switch to the neck pickup. Turn the tone knobs all the way up, then bring them down until you hear a significant drop in treble. The volume knob on the guitar should be kept relatively low, and instead, crank the volume on the amp if you need more noise. Next, dial down the low mid-range setting on your amp fairly low. The high mid-range setting should be turned down a little, but not as much.
Use an effects pedal designed to make an electric guitar sound like an acoustic. Boss is one company that makes a quality acoustic tone pedal. Since these pedals hook up inline with your guitar cord, they can be toggled on and off with the flick of a switch. Acoustic simulation pedals can even be daisy chained with other pedals, such as distortion, so you can switch between acoustic and over-driven guitar on the fly.
Install acoustic mimicking pickups on your guitar that are designed to only pick up certain frequencies. Replacing only one pickup will allow you to, for example, switch from an acoustic neck pickup, to an electric bridge pickup, with a flick of your selector switch.
If you really want an acoustic sound, consider just buying a second guitar for when you play acoustic songs.
If you are not experienced when it comes to working on guitars, leave electronics modification to the professionals. Multiple guitar modifications may cost more than a budget acoustic guitar would.