Google has begun an emphasis on going beyond removing spam and has started targeting low-quality sites. They frequently change their search algorithms, so you may find that something that was working one week has your site not showing up in search results at all. How can you avoid being dropped?
Well, the easy answer is that you should make quality content. What does that mean exactly? It means you should avoid all of the usual Google don'ts, such as copying content from other sources, creating link farms, or using automated spamming tools. It also means that Google has become increasingly sophisticated at guessing whether you're writing something for people or for Google. Do you use natural language as you write, or are you trying to cram in a few more keywords?
You still need to optimize your pages. You do still need to be found in Google, so you can't ignore search engine optimization entirely.
Just as search engines shouldn't be your only focus, search trends should never be your only compass. Lots of writers do keyword research to decide what to write about and which terms to use, and this is useful research. However, you're writing about a topic only because it's popular in search, you're probably going to run into problems. That doesn't mean you shouldn't round out a website about cats with a website about hairballs if you find search demand, but don't write content about lemurs.
Once you get beyond basic optimization, think of yourself as writing content for links on Facebook. That's probably a realistic goal for getting your content noticed these days, anyway. Facebook has become more popular in terms of Web traffic than Google's homepage in the US, and if you get a good viral link, that link can generate a lot of traffic. However, someone is not going to link to your page from Facebook unless your content stood out, whether it was informative, entertaining, or thought-provoking. In other words, quality content.
Watch where you publish. Google is cracking down on content farms. Here's the kicker. As of the time I write, they really haven't defined what a content farm is other than to say they are sites with "shallow or low quality" content. Although non-Google opinion on the definition may vary, my sense is that this centers more around sites that do things like take small snippets of long Wikipedia entries and optimize the page around a specific search phrase. That's content that is neither original nor deep, so Google would penalize this. However, there's a lot of chatter around whether or not other sites would qualify as "content farms" and just how much content it takes to go from "shallow" to quality.
If Your Site Is Dropped
What if you've been playing by the rules (or so you believe) and your site is unexpectedly gone from Google search results? Well, you can appeal. Go to Google's Webmaster Central and apply to have your site reconsidered. I can't guarantee that it will be either swift or painless, but at least Google does provide some recourse.