Well, I'm not sure if this is what your looking for, but there's a really old arcade video game called Q*Bert. I don't think there is any actual "video game" (like an x-box game) that exists at this moment
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Xmen
There are tons of games that start with H the most well known is the Halo series. If you want to know video games that start with H go to this website they have them listed: http://www.dmoz.org/Games/Video_Games/H/
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