Are there any verses in the Quran about personal protection, any verses that says we need to avoid unnecessary harmful acts?
Two of the popular verses that comes to mind are Al Baqarah verse 195:
And spend in the way of Allah and do not throw [yourselves] with your [own] hands into destruction [by refraining]. And do good; indeed, Allah loves the doers of good. Source: http://quran.com/2/195
and An Nisa verse 29:
O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful. Source: http://quran.com/4/29
Both verses are usually used as the basis for Muslim to refrain from smoking or any other harmful things.