Certain kinds of GOTOs are indeed proven mathematically to be necessary to write certain programs, in the sense that eliminating the GOTOs can be done only by making the program more inefficient, i.e. by increasing the number of executed instructions and the amount of memory that is used.

Because of this, any decent programming language must include GOTOs, but in many modern languages they are not named GOTOs, because of the bad reputation of the word.

For instance the language Scheme does not have GOTOs, but it has mandatory tail call optimization, which means that a "tail call" is just an alternative name for "GOTO". For example, this allows the writing of a state machine in Scheme, exactly like it would be written in a language with GOTO, but using tail calls instead of GOTOs.

Other languages have labelled loops and they allow exit a.k.a. break with a label and next a.k.a. cycle a.k.a. continue with a label. Such instructions with labelled targets are just GOTOs with a bad placement of the label, which makes reading the source more tedious than with a classic GOTO.

For providing the benefits of GOTO, a restricted variant is sufficient, i.e. a GOTO that may jump only forwards and which cannot jump inside nested blocks.