I've seen many websites and many networks on the web that all have links that allow users to "Like" them on Facebook or to follow them on Twitter. So, why doesn't a big network like StackExchange have such links on their pages? What are the reasons behind this? I'm curious and want to know.
As adamjford points out, most Stack Exchange sites have a Twitter bot (click the little Twitter icons on this page to find them) and there is a global Stack Exchange bot as well. House ads are run for them, such as this one, to aid with discovery.
For individual questions, the SE 2.0 sites do have share links.
We don't mug for "Likes" on an entire site (or the network) because it's both obnoxious and pointless. The interesting bits are the questions and answers, so we constrain advertising to them.
Personally, I sort of hate these share/like/re-tweet/whatever links you find everywhere on the internet. However, a reasonable number of users want and use them so we provide them where they make sense in an unobtrusive manner*.
*You'll note that we don't embed iframes or third party scripts on page load for any of them, as that negatively affects page load times.
I guess that's because Stack Exchange is a lot of things, but not a social network (chat feature notwithstanding).
Therefore, the usual services associated with that medium are not really in the scope of the site. Requests for social networking features, as interestingly controversial as they might be, are usually turned down.