On a live site, let's say there is a page that is really outdated with old information.
Is it ok to just delete it? Or do I have to setup an Apache redirect or do a 404 or something special for the web crawlers?
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Make sure your web server returns a 404 for deleted resources.
That is enough.
From the official Google Web Master Central blog:
Q: Do the 404 errors reported in Webmaster Tools affect my site’s ranking?
A: 404s are a perfectly normal part of the web; the Internet is always changing, new content is born, old content dies, and when it dies it (ideally) returns a 404 HTTP response code. Search engines are aware of this; we have 404 errors on our own sites, as you can see above, and we find them all over the web. In fact, we actually prefer that, when you get rid of a page on your site, you make sure that it returns a proper 404 or 410 response code (rather than a “soft 404”). Keep in mind that in order for our crawler to see the HTTP response code of a URL, it has to be able to crawl that URL—if the URL is blocked by your robots.txt file we won’t be able to crawl it and see its response code. The fact that some URLs on your site no longer exist / return 404s does not affect how your site’s other URLs (the ones that return 200 (Successful)) perform in our search results.