We describe a simple method for generating new string:solutions for which t
he brane worldvolume is a curved space. As a starting point we use solution
s with NS-NS charges combined with two-dimensional CFTs representing differ
ent parts of spacetime. We illustrate our method with many examples, some o
f which are associated with conformally invariant sigma models. Using U-dua
lity, we also obtain supergravity solutions with RR charges which can be in
terpreted as D-branes with non-trivial worldvolume geometry. In particular,
we discuss the case of a D5-brane wrapped on AdS(3) x S-3, a solution inte
rpolating between AdS(3) x S-3 x R-5 and AdS(3) x S-3 x S-3 x R, and a D3-b
rane wrapped over S-3 x R or AdS(2) x S-2. Another class of solutions we di
scuss involves NS5-branes intersecting over a 3-space and NS5-branes inters
ecting over a line. These solutions are similar to D7-brane or cosmic strin
g backgrounds.