The direct equivalent would be
as in "wiedersehen", "wiedergeben", "wiederholen".
However, you cannot use "wieder-" productively by glueing it in front of arbitrary other words as in "*wiedersenden", "wiederkochen", "wiederprüfen".
Such neologisms would probably be understood, but they tend to sound awkward, unless you have a very specific context and know what you are doing.
Let's test using "wieder" to render English "re-" on some random examples. (Attention, this is experimental, just in order to test to what extent the "wieder-" prefix can be used productively.)
redo --> wiedertun (?) - As "redo" would rather mean "do something again, but in a better way", I think "wiedertun" is not a good fit. "Etwas wieder tun" would mean "do something exactly the same way".
reinterrogate --> wiederbefragen (?) - This could perhaps be used. I imagine police officers who have interrogated a suspect now planning to interrogate him or her again. They could write: "In diesem Falle ist dringend eine Wiederbefragung erforderlich", but this would be very bureaucratic style.
reevaluate --> wiederprüfen (?) - The word would be understood, but would be unusual. The usual way to express "reevaluate" would be "nochmals prüfen".
Note 1: One can go into lenghty discussions about writing words together or separated, and whether or not this carries a difference in meaning, see "wieder geboren" vs. "wiedergeboren" or "wieder verheiratet" vs. "wiederverheiratet".
Note 2: for the variety "wider" (without e) see fdb's answer on this page.