Just as all software has bugs, all websites have dead or broken links. Mistakes happen, content changes, file names and locations change, and external links change. Until you have checked links for some period of time and learned what breaks them you're likely to repeat most of the classic mistakes on a regular basis.
Link checkers work much like a search engine spider. They "crawl" your website looking for internal and external links that are broken. Crawling is recursive, meaning that the spider builds a tree of links leading from page to page until all branches have been explored. Spidering continues until it reaches a defined termination point. For example, when all internal branches have been examined, or when all first level external links have also been examined. A good link checker also produces broken-link reports that enable you to determine where the broken link is, and why the link is broken.
Xenu's Link Sleuth [1] is the only free link checker that does the whole job. It's simple, small, fast and accurate. It takes a while to learn how to use Xenu's Link Sleuth, and it can be daunting to understand the reports, but if you stick with it you'll come to appreciate the excellent job it does.
The LinkChecker [2] extension for Firefox works well, but it only checks one page at a time. However it's useful when you want to do a quick check.
REL Link Checker Lite [3] can do the basic task, but is limited to 1000 links, so you need to work in one sub-directory (if you have them) at a time for larger sites. It's hard to learn how to use RLCL, but it's easy to use once you figure it out. HINT: Use the "Retrieve..." button to get started.
If you want an alternative, check out the web-based FreeFind [4] free search service, which crawls your website to populate their search engine. When finished FreeFind provides a very complete spider report, which shows you all the broken links. You can set the frequency of updates, and thus how often you get the report.
[1] Xenu's Link Sleuth
Website: http://home.snafu.de/tilman/xenulink.html
Download link: http://home.snafu.de/tilman/xenulink.html#Download
Author: Tilman Hausherr
Current version: 1.2j
Version date: October 8th, 2007
Download File size: 545 KB
License: Unrestricted use freeware
Operating systems supported: Windows 95/98/ME/NT/2000/XP,
Additional Software Required: WININET.DLL
required, usually present in Windows
64 Bit version available: No
Portable version available: No
Non-English languages supported: None
Other relevant information: There is no intrinsic limit on the number of links that can be checked. The number of levels seems to be limited to 999.
[2] LinkChecker
Website: http://www.kevinfreitas.net/extensions/linkchecker/
Download link: http://www.kevinfreitas.net/extensions/linkchecker/linkchecker.xpi
Author: Kevin A. Freitas
Current version: 0.6.1
Version date: November 3, 2006
Download File size: 36KB
License: Unrestricted use freeware
Operating systems supported: Windows / Mac / Linux
Additional Software Required: Firefox
64 Bit version available: n/a
Portable version available: n/a
Non-English languages supported: n/a
Other relevant information: This is a Firefox add-on
[3] REL Link Checker Lite
Website: http://www.relsoftware.com/
Download link: http://www.download.com/3000-2181-9426104.html
Author: REL Software
Current version: 1.0 (Build 180)
Version date: 2002
Download File size: 730KB
License: Unrestricted use freeware
Operating systems supported: Windows 95/98/Me/NT/2000/XP
Additional Software Required: none
64 Bit version available: n/a
Portable version available: n/a
Non-English languages supported: n/a
Other relevant information:
[4] FreeFind Web Search Engine
http://www.freefind.com/