Subquery Returning Multiple Rows And Update

This is a surprisingly common one I've found on the web...even on devshed forum

I am updating one table from another (Updating Table A from Table B):

Table A
ID, Value
-- -----
1 A
1 A
2 B

Table B
ID, Value
-- -----
1 Animal
2 Box

Table A (modified)
ID, Value, Name
1 A Animal
1 A Animal
2 B Box

No I need to update a new column in Table A with the value in Table B.Value where the ID's from both tables match. Problem is: When I do this I get multiple rows and hence Oracle won't let me update this column. Now, I keep reading that for these types of updates, there has to be a one-to-one relationship...

Is this true...is there anyway of telling Oracle to update wherever it finds that ID, regardless of how many duplicate ID's there are?

This is quite a frustrating problem and most of the sites that I've looked for solutions try get the query one-to-one...problem is...with my table sets it's impossible to do that - I need to update wherever the id's match (even if it return multiple rows).