What are some examples of website/blog success?

There are hundreds to thousands to mention. See thisiswhyiambroke.com (a good example)

I found this a particuraly good read How I built a top 100 blog in 12 months. He gives you the detail on exactly how he got it earning good money within 12 months.

You can find another one here which should motivate you to turn off your TV: My Income Reports

Almost all of those will be websites with some kind of opt-in, and the monetization will be very closely connected with the site's associated email activities.

In the long run, if wanting to earn a living from internet marketing, it will probably help you to try to give up your current perception of websites as "income-producers": for most marketers earning a living, most of the time, it isn't just the website that produces the money: it's all the other things (especially, but not only, the listbuilding and communications) that they do, which you can't see just by looking at the website, and all the other learning-curves they've successfully negotiated, and all the other skills they have.

Fair enough ... I first made $3,000+ in my fifth month, and I considered that to be "earning a living" (though at the time I didn't yet know whether it would continue in future months). Like so many other people here, I didn't start earning anything worth talking about until I got into list-building. From reading this thread, and your other posts, I urge you to start thinking about why and how it's mostly the aspiring marketers who build lists and learn email marketing skills who go on to make a living from it, and mostly the ones who don't do those things who make up the very high failure-rate in internet marketing.

It isn't just about "websites".

(In my opinion it isn't even mostly about websites.)

Is it a good idea to spend some time on building a mailing list ?
Without Building a List, How Consistent is Your Income from Affiliate Marketing
Does anyone even make money online without an email list?

It will take months or years to establish yourself, so building your online presence needs to be a labor of love -- at first. Emphasize content and a social media presence.

Take a look at what Pat Flynn has built for himself and then ask yourself if you have what it takes to do something similar.

Smart Passive Income

*Note - Pat Flynn has never put a single affiliate link in any of his emails (upon last I checked) and makes no direct income from that list.

I've started a series of case studies on successful affiliate sites, there's only 2 so far but both make far more than the $1000 to $3000 you talk about...

Forget 'Surviving' Find Out How One Blog Makes $1 MILLION Per Month : NicheHacks

[Case Study] How To Create A $20,000+ p/m Affiliate Site Like Thisiswhyimbroke.com - NicheHacks : NicheHacks

More Example on
problogger.net
copyblogger.com
roadtoblogging.com
qcblogging.com

Patt Flynn of Smartpassiveincome.com has built his blog up to making over $70,000 a month. He posts detailed income reports every month on his website.

A good product(s) A membership site, some good affiliates and a product launch with someone known in the business, should take you from nothing to a regular income of a few thousand a month (or more) more or less over night.