There are tons of things that throw exceptions in the standard library with no alternative. std::bad_alloc can get thrown from half the standard library (and it's a lot less implausible than new throwing, because of address space exhaustion on 32-bit). Any constructor that takes input that can be invalid has to throw (e.g. giving a malformed regex to std::regex).

The really obnoxious ones are std::stoi, stol, etc. which were added in C++11 as a replacement for strtol and friends, but throw on overflow/invalid input instead of returning a result type or a bool with out parameter.