In languages like C, unsigned integer overflow reliably wraps around;
e.g., UINT_MAX + 1 yields zero.
This is guaranteed by the C standard and is
portable in practice, unless you specify aggressive,
nonstandard optimization options
suitable only for special applications.
In contrast, the C standard says that signed integer overflow leads to undefined behavior where a program can do anything, including dumping core or overrunning a buffer. The misbehavior can even precede the overflow. Such an overflow can occur during addition, subtraction, multiplication, division, and left shift.
Despite this requirement of the standard, many C programs and Autoconf tests assume that signed integer overflow silently wraps around modulo a power of two, using two's complement arithmetic, so long as you cast the resulting value to a signed integer type or store it into a signed integer variable. If you use conservative optimization flags, such programs are generally portable to the vast majority of modern platforms, with a few exceptions discussed later.
For historical reasons the C standard also allows implementations with ones' complement or signed magnitude arithmetic, but it is safe to assume two's complement nowadays.
Also, overflow can occur when converting an out-of-range value to a signed integer type. Here a standard implementation must define what happens, but this might include raising an exception. In practice all known implementations support silent wraparound in this case, so you need not worry about other possibilities.