Modern C (from C99 onward) introduces a few families of sized types -- [u]int[_least|_fast|][8|16|32|64]_t. The non-least-or-fast types are not guaranteed to exist (e.g., int8_t is optional because implementation may be unreasonable on a 24-bit DSP with no sub-word operations), but the _least and _fast types are generally what you want anyway, unless you're relying on unsigned overflow behavior.

In my experience, modern code is either written almost entirely in terms of sized values like int32_t (when assuming a "normal" platform), or almost entirely in terms of _least/_fast values (when going for maximum portability). The only case that "naked" int/long is still common in this model is in a few specific uses such as loop indices where it's idiomatic.

The _fast and _least types are especially interesting, pragmatically. "int_fast8_t" means "I need a signed value that can store values between -128 and 127, doesn't have defined behavior on overflow, and is allowed to fill a register / use a word worth of memory." "int_least8_t" means "I need a signed value that can store values between -128 and 127, doesn't have defined behavior on overflow, and I am likely to have a significant number of these in memory so please pack them as efficiently as reasonable." (And of course we have bit packing when we need to pack more efficiently than reasonable; bit-packing with int_fast8_t allows you to represent "I need this to take exactly 8 bits of memory, whatever it costs compute-wise, because I'm basically filling memory with these.")

In general, I find that these types give modern C a good balance between declaring requirements on types and not overly trying to control their size.