The answer is an:
HTTP 404 Error Page
I appear if things are broken,
If attempting to access a site, and the page is not found, or the server is not running something (or various other reasons), a 404 error page will appear.
I'm not there if things are flawless,
While not necessarily true, if you don't get a 404, I think the OP is referring to the chance that you're getting a 200, indicating that everything is working correctly.
But you can track me,
It's possible to use tools that crawl webpages to track dead links, or, in the case of a live site, like a forums, will check the link as the page is rendered. (Often via a cache)
I'm not wanted,
No one wants to get the dreaded 404 error page.
I'm clueless,
Apparently 404 has become slang for clueless
in the UK.
I'm different to all,
Most every site has a different 404 error page (unless using something like an initial PHP or IIS install, and they have not changed it.)
You can't touch me by hand.
You...can't touch a 404 error page. Unless you print it out and no one wants to know about that, anyways.
HINT 1:
I can go from 0 to 20.
The HTTP 404 error has 20 sub-statuses ranging from 404.1 to 404.20.
HINT 3:
Some websites report a "not found" error by returning a standard web page with a "200 OK" response code, falsely reporting that the page loaded properly; this is known as a soft 404.
HINT 4:
Humor is used on me (but not always)
Many 404 pages are humorous to lighten the mood of getting a dead link.