The whois records of the domain names,
the DNS records of the domain names,
or the web sites on these domain names?
For the whois records, many domainers run their own tools, which monitor the status of the domain names, mainly the time of the expiration, the redemption period, the pending delete period, and so on. Such tools may be used on the desktop machine, or on the VPS hosting, which is more convenient. The more domains should be monitored, the more IP numbers such software will need for the requests from the whois servers. But such tools are usually not purposed for the public.
For the DNS records, such tool is easy to write, and may use the cheapest VPS hosting.
For the web sites on the domain names, there exist on the Net many monitoring services, from the free versions, to the very expensive versions, which can monitor the content of many sites for the existence of the specified content, and alert the user about the changes.
All such tools usually require to configure in advance, what you want to monitor. If you want to find the changes, which were before your desire, then this may be available with the same tools, if these tools keep the archives of their information. Such archives may be available on request.