You should always be self-conscious. But first, what does it mean to be self-conscious? Well, quite literally, it means to be conscious of self. So, let's break it down one word at a time. "Self" is you; your mind and your body and your constant state of being. To be "Conscious" is to be aware; cognitive perception. Put the two definitions together and: to be "self-conscious" is to be aware of your mind, body, and constant state of being & existence. The widely accepted stigma of self-consciousness is that you feel ashamed and embarrassment. This is simply untrue.
This view of self-consciousness is a falsely dichotomous perception that you cannot both feel embarrassed and procure confidence, simultaneously. There is a deep contrast between unadulterated shame and self-consciousness. Shame is limited and breeds self-loathing, self-consciousness is infinite and engenders humbleness. The importance of being self-conscious is that everyone reaps the benefits of your personal awareness. We are not naturally aware of our own thoughts and perceptions; it is not within our nature to put ourselves in another's state of mind. Instead, we are naturally self-centered and unconscious individuals.
For example, when we are in traffic and cursing the names of those which cut us off and/or speed past us impatiently, we are not fully aware that all we are perceiving is our self-centered nature that someone else is getting in our way. We don't think of their story or that they may be rushing their pregnant wife to the hospital because she's in labor. Although that is an unlikely happenstance, it is possible. So, how does self-consciousness play a part in this? While it is natural to be unaware of things that are seemingly trivial, this is what it means to be self-conscious. To live our lives aware of how our actions affect others and, ironically, to live our lives consciously in other people's state of mind. It's easy to flip off or curse at the person in traffic who cut you off, it's simply how we subconsciously act upon these things. However, it isn't good to act self-indulgent, searching for instant gratification by spewing anger out of frustration simply because it didn't fit into our own self-centered perception.
Furthermore, it isn't good to cut off another person, though it may seem easiest to us in our own little egomaniacal worlds. Look, you might be thinking this is ridiculous and asking yourself why am I listening to this guy telling me how to drive my car, but, it isn't limited to driving, I'm simply using a tangible experience to show how we can become more self-aware persons. I know, it's difficult to notice the negativities of our actions beyond our own periphery; it isn't in our nature to look past our own little bubble, but please, try to, if you are able to.
Before I act upon anything, I tend to try and look at my actions at every possibly angle before committing. Occasionally, I piss people off immensely, however, I always look at how I can better society with my actions and I always look at how I can make a positive impact, sometimes that calls for making the tough decisions and not doing what you want to do but what is necessary, which usually means doing something that is not instantly gratifying. I live my life in perspective, not just my own but everyone else's and I challenge you to do so as well. This is why it's good to be self-conscious of ourselves, and this may make us feel embarrassed when we recognize how unconsciously focused we are on ourselves, but that's good! Just don't fall into that hole of self-loathing, all that is self-absorption clothed in false humility.
Please, I beg you, hear my call to compassion. Most likely you might tell me "good job" and temporarily, or even falsely, admire me for writing this analysis but then continue to unconsciously live your life without self-consciousness. I know it takes a lot of energy and determination, but please, try to. If it doesn't work out for you then I don't blame you, I don't think it's natural for almost anyone to live in the eyes of others, but it won't hurt to try. If you can see yourself objectively, then there is infinite growth. We may never be perfect, but we can strive to be virtuous.