So, you want your site to show up as high as possible on Google. Join the club. 20 gazillion other websites are clamoring for the same thing. And guess what? Google has its own agenda. They don't care whose site comes up on top--whose business gets the free advertising. What they want is to give their visitors the best possible search results--to show them the sites that they're most likely to be interested in. So when overzealous search engine optimizers put the quality of their search results at risk by gaming the system, Google doesn't get mad, they get even by penalizing the site with the dreaded "PR0". Bye bye top position.
Which raises the question, "Will Google penalize me if I _______?" (Enter your favorite SEO technique.) Depending on what you put in the blank, the answer may be yes, or it may be no, or it may be maybe or not yet, but maybe later. Since not all of the answers are known, and since Google may find new things to penalize tomorrow, you should follow this rule of thumb in all of your SEO efforts: "Don't be evil." (Sound familiar? That's Google's informal corporate motto.) In other words, don't do anything "tricky" like posting invisible links that only the search engines can see, joining link farms that create links between totally unrelated webpages, etc., etc.
Obviously, not all SEO techniques are at risk of running afoul of Google's ever evolving algorithms. Any technique that (without trickery) helps Google figure out what your site is about, helps Google figure out which websites have the most useful and popular information, etc.--ie., helps Google to meet their agenda--should be safe. So yes, put the keywords that people interested in your site will likely search for in header tags (h1, h2, etc.). Yes, use those keywords often in the page body (but don't contort your copy beyond readability to overstuff with keywords). Yes, encourage people linking to your page to use those keywords in the links. And so on.
Nobody knows for sure what Google will decide to penalize tomorrow. So to be safe, you'd better be scratching Google's back, and not stabbing it.