As others have said, proceed with caution! Assuming you've already used a top email list hygiene provider like Fresh Address or Webbula (if you haven't, you might need to clean it again), here's what I suggest you do next:

1) Interrupt your pattern of sending content newsletters with either a preferences or general survey, ideally with an incentive for completion (random prize drawing works well). At this point, sending a campaign people will be HIGHLY MOTIVATED to open and click is key, since leading ISPs such as Gmail and MSN are increasingly using engagement metrics to determine whether your email keeps getting delivered or gets junked. Also, conditioning a pattern of response early is important to getting people to engage on a regular basis.

2) Vary your messaging to include other campaigns than just newsletters. People grow immune to repetition. What stand-alone messages can you work into the schedule? Maybe a weekly spotlight on a featured piece of content, interview with a subscriber, weekly trivia, etc. These are all great for engagement.

3) Keep a strong eye on your deliverability and reputation as an email sender. Look into ReturnPath's services.

4) As far as "dropping email addresses that have not engaged with any campaigns" consider your options and define "engagement". What are the actions and thresholds of activity that constitute "engaged" - is it no opens/clicks in 30 days? 90 days? longer? You don't say if you'll be wiping those from your list and never emailing again, dialing back volume, or suppressing and contacting with a reactivation or re-opt-in campaign. If you decide to no longer email inactives, try targeting them in other channels like via FB custom audience targeting or Live Intent.

Need more help or a long-term strategy? Contact me - it's what I do.