Asrujit, that makes sense, but in my particular example, I am referring to accessing the database through a single source, and still seeing upwards of 5 or more connections. For instance, I had everyone log off last night a little early so I could make some changes to some fields that we have in our feature classes, and I had 5 connections that were time stamped at various times throughout the day. Instances that I was no longer using or even had open. At that moment that I was looking, the only thing that I had open was ArcCatalog, and I was only accessing the database through a single connection file.
All in all it doesn't really create a problem for me, as I can simply break the locks to ensure that my current instance is the only connection, but I really just want to be sure that there isn't some underlying problem that we are having, or if by breaking those locks I may be harming something that took place earlier in the day.