Are incrementers / decrementers (var++, var--) etc thread safe?

No, incrementing is not thread-safe. Neither are the INC and DEC instructions. They all require a load and a store, and a thread running on another CPU could do its own load or store on the same memory location interleaved between those operations.

Some languages have built-in support for thread synchronization, but it's usually something you have to ask for, not something you get automatically on every variable. Those that don't have built-in support usually have access to a library that provides similar functionality.

In a word, no.

You can use something like InterlockedIncrement() depending on your platform. On .NET you can use the Interlocked class methods (Interlocked.Increment() for example).

A Rob Kennedy mentioned, even if the operation is implemented in terms of a single INC instruction, as far as the memory is concerned a read/increment/write set of steps is performed. There is the opportunity on a multi-processor system for corruption.

There's also the volatile issue, which would be a necessary part of making the operation thread-safe - however, marking the variable volatile is not sufficient to make it thread-safe. Use the interlocked support the platform provides.

This is true in general, and on x86/x64 platforms certainly.