I suppose like many people, I grew up thinking that repentance of one's sins requires guilt, anguish, even self-loathing. That faintly offended me — I felt I was living a reasonably good life, all in all, and I couldn’t understand why any of those feelings were called for. (Yes, I know, some people will say that my lack of these feelings was proof positive that I was indeed a sinner – QED, I guess.)
A few years ago, I learned that I may have misunderstood what repentance was all about. I read that the original Greek word in most places in the New Testament, which is usually translated as “repentance,” is metanoia, which according to this Greek lexicon means a change of mind or attitude. (Disclaimer: I know only a few words of Greek, so I might be totally missing the point.) Somewhat to my surprise, this change-of-mind meaning also shows up in English-language definitions of “repentance,” such as this one.
Does remorse still play a part in repentance? Unquestionably. A change of mind or attitude can certainly lead to remorse about one’s former mindset, and about the consequences stemming from it. Or, it might work the other way around – remorse could be a motivator for a true change of mind. In his second letter to the Corinthians, Paul says that “Godly sorrow brings repentance that leads to salvation and leaves no regret” (2 Cor. 7-10).
I ran across a few interesting articles in a quick Google search. See, for example, this article about repentance and its meaning, from the perspective of a devout Christian. See also this list of Web writings on related subjects.