We consider three examples of Lie-Rinehart algebras:
1. A canonical construction of a Lie-Rinehart algebra over a Poisson algebra A.
2. A generalization of the first example, considering A to be a Jacobi algebra.
3. Further generalizations of the first two examples, that involve introducing an endomorphism of the underlying commutative algebra A.
Moreover, based on results by J. Huebschmann, J. H. Lu and I. Vaisman, we explain that we can construct a Hopf algebroid structure on the enveloping algebras of both Lie-Rinehart algebras constructed in the examples above.