This is a very debatable area and can vary as per the type and nature of one's business and customer needs.
However, the following may be considered as some handy tips based on past experiences with projects involving 'content-heavy' websites. It should be noted that these are personal view points and should not be deemed to be universal industry-standard or globally accepted rules.
Stop and think twice before starting off with a WCM system if:
Most of the data on the website is fairly static and less prone to updates.
If you do not require making frequent content updates on the site, try and come up with an alternative mechanism for managing the content. Using an automated content management system in such scenarios might turn out to be overkill and result in extra and unwanted costs.
You have neither the time nor the money for training the employees.
For smaller firms running on low revenue margins, purchasing a CMS system, getting it installed/set...