The ring of entire functions on the open complex plane
For instance the ring of analytic functions on any non-compact Riemann surface is a Bézout domain (Helmer 1940), and the ring of algebraic integers is Bézout.
Equivalently, a Prüfer domain may be defined as a commutative ring without zero divisors in which every non-zero finitely generated ideal is invertible.
Bourbaki lists fourteen of them, (Gilmer 1972) has around forty, and (Fontana, Huckaba & Papick 1997, p. 2) open with nine.
As a sample, the following conditions on an integral domain R are equivalent to R being a Prüfer domain, i.e. every finitely generated ideal of R is projective: More generally, a Prüfer ring is a commutative ring in which every non-zero finitely generated ideal containing a non-zero-divisor is invertible (that is, projective).