How far can memory leaks go?

No. Operating systems free all resources held by processes when they exit.

This applies to all resources the operating system maintains: memory, open files, network connections, window handles...

That said, if the program is running on an embedded system without an operating system, or with a very simple or buggy operating system, the memory might be unusable until a reboot. But if you were in that situation you probably wouldn't be asking this question.

The operating system may take a long time to free certain resources. For example the TCP port that a network server uses to accept connections may take minutes to become free, even if properly closed by the program. A networked program may also hold remote resources such as database objects. The remote system should free those resources when the network connection is lost, but it may take even longer than the local operating system.

The C Standard does not specify that memory allocated by malloc is released when the program terminates. This done by the operating system and not all OSes (usually these are in the embedded world) release the memory when the program terminates.

As all the answers have covered most aspects of your question w.r.t. modern OSes, but historically, there is one that is worth mentioning if you have ever programmed in the DOS world. Terminant and Stay Resident (TSR) programs would usually return control to the system but would reside in memory which could be revived by a software / hardware interrupt. It was normal to see messages like "out of memory! try unloading some of your TSRs" when working on these OSes.

So technically the program terminates, but because it still resides on memory, any memory leak would not be released unless you unload the program.

So you can consider this to be another case apart from OSes not reclaiming memory either because it's buggy or because the embedded OS is designed to do so.

I remember one more example. Customer Information Control System (CICS), a transaction server which runs primarily on IBM mainframes is pseudo-conversational. When executed, it processes the user entered data, generates another set of data for the user, transferring to the user terminal node and terminates. On activating the attention key, it again revives to process another set of data. Because the way it behaves, technically again, the OS won't reclaim memory from the terminated CICS Programs, unless you recycle the CICS transaction server.