Since I have some opinions on the subject, I though I’d add a little.
As a pastor for a number of years, my professional capacity and sensibilities have overcome my introversion when it comes to greeting people. For many years now I have used the time before worship to “work the crowd” – connect with the people in attendance. I try to meet all the people I don’t know and at least greet everyone else. (Obviously this is easier in a small congregation.) But that’s BEFORE the worship “service” starts.
In my United Methodist tradition the biggest complaint about greeting times is that they interrupt worship. My take on the practice is different, however. I see the greeting time as a an opportunity for the Body to come together, connecting with each other. Our culture is so prone to individualism that even in a worship “service” the focus in on the single worshiper. We think the people around us need to mind their own business so I can worship. In the greeting we’re forced to acknowledge the people around us. We’re not forced to connect with them and become co-workers, but as leaders we can certainly invite people to connect and become co-worshipers.