The desire to alter the state of consciousness is a common one among humans (and many other animals as well). The following are drug-free ways to alter your state of consciousness (though I'd imagine a lot of them would be greatly enhanced while on drugs). Try doing two or more at once for a greater effect.
These devices will flash at a certain rate and when viewed with the eyes closed are said to trigger a hypnagogic (near sleep) state. If you suffer from epileptic seizures don't try using a dream machine or it could trigger a seizure. You can view an online one at http://www.netliberty.net/dreamachine.html. The flashes are supposed to stimulate your optic nerves creating alpha waves in your brain. Changing the colors and/or frequencies also has an effect, so be sure to experiment.
Lucid dreaming is dreaming while being aware that you are dreaming, thus being able to control the dream. Dreams are an incredible playground, you can do whatever you want with absolutely no consequences and you can plan ahead to go wherever you want in the dream. How to induce a lucid dream is in itself a whole other node.
If you have a ton of money and/or time you can build a full sensory deprivation tank. For the rest of us, a bathtub with salt, the light turned off and ears submerged (preferably with ear plugs) will have to do. The key is to have as little stimulus coming in as possible, so everything is coming from your own mind.
While not everyone will consider it fun, sleep deprivation will definitely induce an altered state of consciousness. It's hard to come up with hard numbers, but expect to wait at least 48 hours for the hallucinations to start. Caffeine should be very useful.
Very similar in concept to the dream machine, binaural beats work by having a slightly different frequency in each ear to entrain the brain waves to the difference in frequencies. So if you had 350 hz in one ear and 360 hz in another your brain waves would lean toward 10 hz. Can be combined with the dream machine (make sure they're both at the same frequency) for an added effect. Go to http://www.jetcityorange.com/meditation/binaural-beats.html for a good selection of free beats, you'll need headphones/ear buds for it to work.
Meditation is a way to focus the mind. It's hard to say exactly what meditation is, as there are thousands of different methods. A common method involves focusing on the breath. Regular meditation is said to reduce the need for sleep, in addition to various other benefits. Check out this excellent node to get started.
A common experience among runners is a "runner's high" or a state of euphoria experienced after a certain threshold that varies between different people. While you don't necessarily have to run, you would need to do some form of intense aerobic exercise (walking won't work) continuously for a prolonged period of time. The downside to this is you must already be in decent shape to run long enough.
Yes I know caffeine is a drug but I don't think it really counts in this case.