Example: Die Ukraine droht Russland nicht, aber die ukrainische Revolution bedroht Putin.
drohen - active:
"Sie droht mir mit Hausarrest."
"Samsung droht Apple mit einer Klage."
drohen - passive:
"Mir droht Hausarrest."
"Dem Windows Start-Button droht das Aus."
bedrohen - active:
"Die Abholzung des Regelwaldes bedroht viele Tierarten."
bedrohen - passive:
"Viele Tierarten werden durch die Abholzung des Regenwaldes bedroht."
Even if you did not ask for passive/active, I think this is important as they might easily get mixed up.
"Drohen" is, as said by Chanz already, to threaten someone or something in any way. "Bedrohen" means that the action/circumstance already has (or has a very high chance to have) an effect that is endangering something.
This might be violence in order to force you to do something ("Er bedroht mich - wenn ich es nicht tue, wird er mich schlagen."), but also similar, but less direct actions - e.g. the forest is not being chopped in order to extinguish any species.
Both drohen and bedrohen share the basic meaning of to threaten
In almost all situations they are perfectly synonymous. There are some subtle differences however.
Ich bedrohe dich.
Without any additional information I would take this to mean that I am threatening to use immediate physical violence against you, whereas
Ich drohe dir.
would "only" imply a verbal threat of future consequences if you don't comply with my demands.
Also, there are differences in the passive use of both forms:
Durch den Klimawandel droht der Meerespiegel anzusteigen.
You couldn't use bedrohen here, but
Der Anstieg des Meeresspiegels bedroht vor allem die Küstenstädte.
Bedrohen implies a more immediate kind of danger, with the possible consequences already obvious to the threatened one. In your example
Die Ukraine droht Russland nicht, aber die ukrainische Revolution bedroht Putin.
the Ukraine did not utter any threats directed at russia, but the revolution itself may be a danger to Putin.
Drohen - means "to threaten someone" and is always directed at a person.
Bedrohen - means "something is threatening" and can be applied to objects as well.
Bedrohen generally takes an object whereas drohen is most often without an object. German verb prefixes often indicate direction, so to speak, with the prefix be- indicating unto something else. Obviously there are exceptions, such as Bestehen, but I think this "rule" would hold up in most cases.
drohen --> active
bedrohen --> passive
Ich bedrohe dich. (Ich drohe dir.)
Du fühlst dich von mir bedroht. But not Du fühlst dich droht von mir.