The glorified global variable - becomes a gloried global class. Some say breaking object-oriented design.
Give me scenarios, other than the good old logger where it
A Singleton candidate must satisfy three requirements:
If your proposed Singleton has only one or two of these requirements, a redesign is almost always the correct option.
For example, a printer spooler is unlikely to be called from more than one place (the Print menu), so you can use mutexes to solve the concurrent access problem.
A simple logger is the most obvious example of a possibly-valid Singleton, but this can change with more complex logging schemes.