I have had times where I'd eagerly sign up for newsletters and updates via email as I want to know everything they know. It came to the point where I have gone down the deep end with subscribing to email newsletters and not able to opt out at times. Repeat offenders such as LinkedIn, MSDN Flash, InfoQ, DeafDigest and so on has stayed clear from my inbox for years now and I only check when I have some free time. Before my phone would buzz all the time with emails and sometimes I gets so much that I would overlook an critical email, especially from my wife. Been chagirned over that and sent to the doghouse.
So that was a few years ago and today I to share with you what I've done to keep my emails in the Inbox to the minimum and keep your phone free to only receive critical emails.
Open offending spam-ish email, at upper right of email, there's a dropdown box, click the down arrow and select "Filter messages like these". Accept default and just click on lower right link "Create filter with this search". Check "Skip the Inbox (Archive it)", and check "Apply the label", dropdown and create a new label "...". I didn't know what to call it, it's not spam per se, but it's not a email I want to be receiving on my mobile phone. So I came up with nothing, aka "...". Finally, click "Create filter", if you want, check to Also apply filter on matching conversations. Repeat as necessary to other emails as they come in then over time you'll be in a bliss.
Outlook: You can use the their two-click Sweep mechanism.
See your non-critical emails disappear our of your consciousness and I guarantee you that you'll find that you will start to ignore and could care less about those emails.