I'm an introvert. And so are many other reasonably bright, well-rounded, effective individuals. So it's not a bad thing. But I do believe that to be most effective, the introverted leader should examine what this personality style can mean in the context of leadership - and know how to leverage it successfully.
(And if you're more of an extroverted leader by nature, this is still worth paying attention to: to lead well you need to understand all types of personalities - including the introverts).
What makes a person more introverted or extroverted? In simplified terms it's about how we process our information and how we 'recharge': the extrovert will often examine his thoughts out loud to others, whereas the introvert is more likely to spend more time alone making sense of his. The extrovert will seek out others as a source of stimulation and energy, and the introvert will be pushed to the edge of exhaustion if she's unable to take refuge in her own solitude. Introverts are typically more socially reserved than extroverts, and their presence can easily be missed in a roomful of people (this is not synonymous with 'shy', however - we're not necessarily shy as much as we are 'quiet and unassuming').
So, then, can an introvert really be an effective leader? Of course she can - but in a rather different way than how we're used to thinking about leaders: most of the politicians and other leaders we see in the public eye are extroverts. This is the type of leader we're used to because they're in front of us every day. They're charismatic, outgoing, and animated. They have a commanding presence. They're the 'people people'.
But it's important for the introverted leader to refrain from trying to emulate the extrovert just because that's what others may expect. Developing stronger speaking skills and making the effort to connect with others in more dynamic ways, for instance, are important things to practice - but trying to be someone we're not is inauthentic. And nobody likes a phony.
(Finding this balance can be a fine line sometimes, but we can always check in with ourselves with this simple question: "Am I trying to be someone I'm not, or am I genuinely trying to bring out the best of who I am and who I could be?")
We all have the ability to stretch our personalities a little; to enlarge them enough to more effectively meet the world head-on, and to operate a little bit out of our comfort zones. The introvert can and should learn to present himself in more outgoing ways as the situation requires - but he should also understand that much of his effectiveness actually lies in his introversion: that his natural tendencies as an introvert also happen to be important leadership qualities.
The introvert's innate leadership qualities are in his tendency to observe carefully and evaluate accurately before engaging a situation; in his habit of formulating his thoughts and planning his message before speaking; and in his ability to quickly cultivate quality relationships.
So, yes, introverts can make great leaders - but they do need to stretch their boundaries in order to be heard in an extroverted world. And just as importantly, they need to recognize and embrace their 'gifts' rather than resent their 'shortcomings'.