Spam is a huge problem. But my experience with the Gmail spam filter has been heavenly; it's been years since I've seen spam in my inbox promising to enlarge my manhood with a Rolex.
The big problem today is opt-in email. I have been actively unsubscribing from email lists for months. But newsletters, special updates, coupon offers, and other email marketing still arrive every day in droves. During the last seven days I have received 14 notifications from meetup.com, 6 Google+ friend requests, 3 Facebook event reminders, 2 notifications from job boards, 2 newsletters from services I've long since stopped using, 2 survey requests for services I've recently used, 1 LinkedIn update, 1 travel advertisement, and 1 airline advertisement. That's 32 emails in 7 days. I never consciously opted into any of these emails and have tried to unsubscribe myself as best I can.
But increasingly, I see emails sent from large, respectable companies  that provide me with no unsubscribe link. Instead there is an insidious trend towards "Managing Preferences," which invariably requires a log in, a brief search to find the unsubscribe option, and a form submit. And after all that am I unsubscribed? Apparently not because I keep getting messages. The companies assure me that I'm off XY email list while seemingly putting me on ZQW list simultaneously. Perhaps most irritating of all, I am spending an increasing amount of time browsing and checking email from my phone, and elaborate unsubscribe workflows thwart my ability to quickly opt out.
As the founder of a web startup myself I do not believe there is anything wrong with emailing customers. I don't even mind that I'm being opted into email lists by default; it actually makes a lot of sense. We did an A/B test a while back to see whether visitors to our site wanted to subscribe to five introductory tip emails . Interestingly, we found that just putting the option to get email--we phrased the offer several different ways-- decreased signups, even though 78% chose to receive them, and getting them vs. not getting them made no difference in conversion past the free trial. Users didn't mind getting email, but they did mind being asked. We derive monetary value from sending customers email, and subscribing users by default causes fewer than 1 complaint per 10,000 emails sent. In summary, a company has every incentive to email its customers, and I don't begrudge those attempts. The problem is that these companies aren't respecting my ability to unsubscribe.
Skritter and CodeCombat newsletters go out to a lot of people every month, and folks seem to enjoy it. We easily get 10x the number of positive responses to our newsletter for every request to unsubscribe. I suspect the reason is that we provide a one-click unsubscribe link that respects people's time and privacy. If my company were 20x larger, we would probably want to send more and different email to customers. But complexity doesn't magic away a company's responsibility to allow innocents like me to easily opt out of their email presence. When a company asks me to "Manage my Preferences," they disrespect my time and fracture my trust.
 LinkedIn and TripAdvisor spring to mind as companies that have foisted this on me just in the past 7 days. I still can't figure out how to make the Trip Advisor emails to stop, even after wandering around the "My Account" section on my laptop for several minutes.
 The tip emails were a series of 5 emails sent to users during their trial periods that introduced them to site features. They were 100% instructional and intended to increase engagement. We didn't put marketing or sales materials in them.