  The well-known Disjoint Paths problem is to decide if a graph contains k
pairwise disjoint paths, each connecting a different terminal pair from a set
of k distinct pairs. We determine, with an exception of two cases, the
complexity of the Disjoint Paths problem for $H$-free graphs. If $k$ is fixed,
we obtain the $k$-Disjoint Paths problem, which is known to be polynomial-time
solvable on the class of all graphs for every $k \geq 1$. The latter does no
longer hold if we need to connect vertices from terminal sets instead of
terminal pairs. We completely classify the complexity of $k$-Disjoint Connected
Subgraphs for $H$-free graphs, and give the same almost-complete classification
for Disjoint Connected Subgraphs for $H$-free graphs as for Disjoint Paths.
