Classifying values by interval

Greetings All!
As is often the case on this list, the answer may well
be under my nose but I can't see it!

I am looking for a "smart" way to do the following.

Say I have a vector of values, X. I set up bins" for X,
say with breaks at B = c(b1,b2,...,b11) covering the
range of X, i.e. bins numbered 1:10. The value x is in
bin i if B[i]<  x<= B[i+1]

What I seek is a vector, of the same length as X, which
for each x in X gives the number of the bin that x is in.

Clearly this can be done in an "unsmart" way by looping
through all of X along with something like

   which( (B[1:10]<  X[j])&  (X[j]<= B[2:11]) )

However, I feel that this naturally occurring task must
have received a smarter solution! The hist() function
already does this implicitly, since it has to decide
which bin a value in X should be counted in. But it
apparently then discards this information, since there
is nothing relevant in the return values from hist().

So is there a "smart" function somewhere for this?

The motivation here is that I have multivariate data,
(X,Y,Z,...) and I wish to study how it behaves in each
different bin for X. So the "bin index", ixB aY, derived
for X can be applied to select corresponding subsets of
the other variables. Rather than doing it the clumsy
way each time, e.g. according to

   Y[(B[i]<  X)&  (X<= B[j+1])]

I would like to have the bin index permanently available
-- for example it allows easy logical combinations of
bins, such as Y[(ixB==j1) | (ixB==j2)], or Y[(ixB %in% ixB0)].