*** UPDATED TO INCLUDE STEFAN GOSSNER's INPUT ***
After updating SharePoint 2013 to November 2017 CU from a previous version you will not be able to open Office documents (Word, Excel, PowerPoint) but other types of documents like .txt and .pdf files can be opened. There is no indication of the error in the ULS log.
November CU brings a breaking update to stssoap.dll. This dll is normally cached in the _app_bin folder of the web application and it does get updated at the 15 hive bin folder but not at the local web applications bin folder.
For example, imagine a web application for portal.contoso.com, on location C:\inetpub\wwwroot\wss\VirtualDirectories\portal.contoso.com80. You will find stssoap.dll in C:\inetpub\wwwroot\wss\VirtualDirectories\portal.contoso.com80\_app_bin\stssoap.dll version not to match the version in C:\Program Files\Common Files\microsoft shared\Web Server Extensions\15\CONFIG\BIN\stssoap.dll.
The main cause for this is that the update was not done properly (i.e. via Wizard or using all the appropriate commands via PSConfig).
Make sure you run the update properly
Always prefer to use Configuration Wizard over PSConfig to update. This command should update the web applications _app_bin:
PSConfig.exe -cmd applicationcontext -install
See more details here.
To emulate all the steps of the configuration wizard in the future, use this:
PSConfig.exe -cmd upgrade -inplace b2b -wait -cmd applicationcontent -install -cmd installfeatures -cmd secureresources -cmd services -install