Nikto
Nikto is an Open Source (GPL) web server scanner which performs comprehensive tests against web servers for multiple items, including over 3500 potentially dangerous files/CGIs, versions on over 900 servers, and version specific problems on over 250 servers. Scan items and plugins are frequently updated and can be automatically updated (if desired).
Nikto is not designed as an overly stealthy tool. It will test a web server in the shortest timespan possible, and it's fairly obvious in log files. However, there is support for LibWhisker's anti-IDS methods in case you want to give it a try (or test your IDS system).
Not every check is a security problem, though most are. There are some items that are "info only" type checks that look for items that may not have a security flaw, but the webmaster or security engineer may not know are present on the server. These items are usually marked appropriately in the information printed. There are also some checks for unknown items which have been seen scanned for in log files.