Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.
Conventional superconductors can be either type-I or type-II.
Niobium and vanadium are type-II, while most other elemental superconductors are type-I.
The most commonly used conventional superconductor in applications is a niobium-titanium alloy - this is a type-II superconductor with a superconducting critical temperature of 11 K. The highest critical temperature so far achieved in a conventional superconductor was 39 K (-234 °C) in magnesium diboride.
Ba0.6K0.4BiO3 is an unusual superconductor (a non-cuprate oxide) - but considered 'conventional' in the sense that the BCS theory applies.