I prefer the earning of respect and trust, personally. I don't know many people and many people do not know me, personally. Those who do know me personally generally trust me (and some trust me waaayyy too much). I don't request it, nor do I demand it. I am human and am prone to making mistakes, however, I will own up to my mistakes when made.
To answer the question, I consider myself trustworthy - although, I do know myself and have known myself for many, many years.

I keep to my word that if I say I will do something, I will do it. If for some reason, I cannot, I will admit that I cannot do it and rescind but I will not promise anything unless I am 100% beyond a shadow of a doubt certain I can meet what I promise.