Android phone? Well I have this Htc vivid droid phone and I downloaded this cool shooting game on it. I played the game nonstop for at least 3 or 4 hours when I started to notice the back of the phone getting hotter to the touch with each passing hour. 5 hours into the game I noticed what seemed like steam/smoke coming from under the battery cover. I opened it up,removed the hot battery and smoke was coming out of small openings from inside the phone. I freaked out and haven't played for that long since. The phone still works but could it have overheated or something?

Just kidding smoke should not come out of phones, unless it is a Native American phone, I heard they use them for smoke signals!
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The manufacturer is supposed to limit either the hardware or the software to prevent the CPU from running at a speed that would generate enough heat to do that.
If for some or other reason it did overheat, there should be a fail-safe to cut the power so as to prevent it from getting hotter and damaging something.
Either your phone is a dud or the HTC Vivid is poorly designed and has none of the aforementioned methods of protection.
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If you rooted it and overclocked it, then it's your own fault (and not covered by the warranty)
...otherwise I'd send it in and see what they have to say about it.
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If it's still covered under warranty I'd actually keep going to see if I can burn it out, then send it in and get a new one that's hopefully not prone to overheating.
No, it's not normal. I think you stop using that phone and report it to the manufacturer. Get a new phone if you can. My old phone used to overheat and the guy told me that was a common complaint. Which caused me to wonder, why was it still being sold? My current phone, on occasion will get hot and make a burnt smell (there's actually a faint smell now), but it has never smoked on me... Yet.