For active fermentation, the release of CO2 will keep Oxygen from entering your fermentation vessel. When that slows down, the chances of Oxygen entering unless it is a large opening is rather small. Generally, there needs to be a driving force of which the concentration of O2 outside the vessel and lack of O2 inside the vessel is very minor. What can induce more O2 egress into the vessel would be large temperature swings, cold crashing, or opening up the vessel frequently to add or remove contents. On the home brew level, there will almost always be some cold side Oxygen exposure unless you have a really well sealed system. The chances of it affecting the shelf life and flavors of the beer is dependent upon the amount of the exposure.
From my personal experience, I don't do anything extraordinary to protect my finished beer from oxygen exposure during bottling. I do try to avoid splashing and mixing of my beer. While I cannot say that there is not some affect on the flavor of aged beers, I have had Munich Pilsners take medals at 10 months in the bottle with no comment about oxidation or flavors related to such.
