Gmail Filters, in conjunction with Gmail Labels is all you need to achieve this. And is very simple to use as illustrated below:
This example illustrate how to take out those Twitter follow invites from your Inbox while allowing you to review them at your own pace.
1. Start by selecting Create a filter next to the search box.
2. In the Subject: field, enter "is now following you on Twitter!" and press Next Step > to continue.
3. Now choose the action you want to apply. You can do anything you want to it, but this is the common things that I do:
3A. Check Skip the Inbox (Archive it). This ensures that it will not show up in your inbox when it arrives.
3B. Create a new label in the Apply the label dropdown, or select an existing label that you would like to apply.
3C. If you are creating a new label, you might want to Also apply filter to conversations below. I guess I had 5000 follows on Twitter since I started using Gmail. Now *that* would be insane if I didn't use Gmail filters!
Don't be alarm if you think that you will never see them again since you have skip the inbox, they still show up in your filter list, and unread items still show up as bold.
I use Gmail filters for pretty much everything, and auto-archive most of the stuff that goes into my inbox, leaving it clutter-free only with important stuff that I need to get to. Here's a list of examples of where you would want to auto-filter:
1. Social network activites. I label all of these with a prefix soc: so they are grouped together nicely in the filter list. Aardvark, Facebook, FriendFeed, Flickr, Picasa, Twitter, or whatever. All gone. Best of all and especially for Facebook activities, I usually can just take a quick glance at the list titles to note the things that require actions, then select all and Mark as Read.
2. Listserv. Do you subscribe to a lot of listserv? Anyone of those IxDA list will turn your inbox into a nightmare!
3. Magazine subscription. I enjoy some of the publication alerts like MKQ and WSJ but they get scary very soon. I like keeping these as email items instead of just reading them in list readers so I can search for them later.
4. Google Alerts. Comes in thousands. Good to know when your stuff get blogged etc. This is especially useful if you license your content via Creative Commons.
5. Keywords. Some times come through in multiple places and does not have a particular subject / email address. Use keywords to bundle them up together.
6. Email addresses. Gmail support retrieving other external accounts. So you can use the same strategy to check your other mails, and also apply labels where necessary.