I logged in to Anexxia's horde guild the other day to see a familiar name in gchat. This individual inspired one of my favorite posts of all time, "When the Raid Leader Says Everyone, This Means YOU."
He'd also led a fairly successful (11/12 in short order) new guild with the birth of Cataclysm. A guild he left in the lurch by selling his account and "quitting WoW." An action that screwed over all those who had built that guild up with him (including leaving an established guild to do so.) That decision seems to have lasted all of a month before he turned up, like a bad penny, in my guild.
How did this happen? Because my current raiding guild is run by someone who doesn't think process of any kind is important, especially such a silly thing as a guild application process.
Now, certainly, not every guild needs an application process. If you only invite friends of existing guildies (and by friends I do not mean some person they just picked up in LFD, something a former guildie of mine was notorious for.) But if you are running an even moderately successful raiding guild, it's a must.
Having a solid application, that asks some hard questions about why the applicant left their former guild and what made them interested in yours is a good way to get a glimmer of how someone will behave in your guild. It also gives their former (or even current) guildies an opportunity to put in a good word, or to tell you that the person is a drama queen who tried to recruit away half the main raiders to form their own guild. Without an application process, you can quite easily end up with a guild full of people who can easily ruin your guild's reputation-- and its team spirit.
An application isn't an insurance policy against recruiting bad apples into your guild, but it certainly can be a great early warning system. Don't step into Firelands without one.