Having multiple domains point to one website is common as a company will buy variations of their main domain name (other TLDs, misspellings) and then point them to their main domain so on the off chance that someone uses one of those variations they still will end up at the company's website.
As far as SEO goes having so many domains pointing to one place is not helpful and can be harmful if done incorrectly. If the domain names pull up the same content as the main domain and no 301 redirect is done or a canonical URL is given then those pages will be seen as duplicate content. At best they will be diluting their presence in the search engines by having their content spread out over so many domains, at worst they will have the duplicate filtered out and possibly have less content in the search results if they can't determine which content is the original content.
Additionally, when a redirect is used it will effectively tell Google that URL no longer exists and has moved to the main URL. So having keyword rich add on domains won't actually accomplish anything.
But if it is all set up properly, either through DNS or 301 redirects in Apache, then it shouldn't be messy or harmful to the site. So if it is messy then it probably is done wrong and really needs to be cleaned up.