Wired doorbells operate on a low voltage via a transformer wired to to the house 110 AC wiring. Failures often start with the transformer which may be hidden. If you bell works at the neighbors but not yours, the transformer is probably the reason. You can determine this by testing for current at the bell or button.
Bottom line is I agree with steve on this one. The wireless bells allow you to install buttons at multiple doors and have a reliable systme with no real work at all.