I was wondering if anyone else does that, and if so, what are some of the rules or limitations you put on yourself?

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I am going to do a Let's Play about this sometime, but one thing I do in The Legend of Zelda for NES is max out my hearts, get the blue right and white sword and such before I hit level 1. That said, that makes level one easier... So. Harder...
Hm.
Well I had a dream with the Legend of Zelda that one could beat it without the sword entirely. I tried it a few times but couldn't seem to crack the nut, but some great souls have.
http://faqs.ign.com/articles/559/559800p1.html
In the Elder Scrolls games, I always set out to make different characters with different stats and different focuses, but I always end up playing a sneaky thief archer/dagger wielder. So I'll frequently put these self-imposed rules on myself to force me to play in a different way. I just love that play style, it's hard not to go back to it, but it's worth it to see all the different ways you can play.
If a game has a difficulty setting, I usually choose the hardest available for my first play through. There's a few games where this doesn't work out; namely the Command and Conquer games, but it keeps things challenging. In games like Elder Scrolls, I try do at least one run though using fists only. There's a strange satisfaction in punching a giant to death.
vdogmr25-- Elder Scrolls unarmed reminds me of this. If you haven't seen this, it's hilarious.
https://www.youtube.com/watch?v=uhBiNx749Zw
MAJOR language warning on this. Don't watch unless you're ok with numerous f-bombs.