Replicate and expand a list

For all versions:

Replace[a2, Append[Thread[a -> b], _ -> 0], 1]

{10, 20, 0, 50, 80, 0}

If you need speed look at Dispatch.

For versions 10.0 or later Association functionality is fast and concise:

Lookup[AssociationThread[a, b], a2, 0]

{10, 20, 0, 50, 80, 0}

Tersely Thread works in place of AssociationThread but it causes a redundant evaluation:

Lookup[Thread[a -> b], a2, 0]

{10, 20, 0, 50, 80, 0}

Fold[Insert[#1, 0, #2] &, b, Position[Map[Position[a, #] &, a2], {}]]

{10, 20, 0, 50, 80, 0}

Probably faster with large lists:

Fold[Insert[#1, 0, #2] &, b, Position[a2, Alternatives @@ Complement[a2, a]]]

The most obvious :

If[MemberQ[a, #], b[[Position[a, #][[1, 1]]]], 0] & /@ a2

{10, 20, 0, 50, 80, 0}