  We study the following general stabbing problem from a parameterized
complexity point of view: Given a set $\mathcal S$ of $n$ translates of an
object in $\Rd$, find a set of $k$ lines with the property that every object in
$\mathcal S$ is ''stabbed'' (intersected) by at least one line.
  We show that when $S$ consists of axis-parallel unit squares in $\Rtwo$ the
(decision) problem of stabbing $S$ with axis-parallel lines is W[1]-hard with
respect to $k$ (and thus, not fixed-parameter tractable unless FPT=W[1]) while
it becomes fixed-parameter tractable when the squares are disjoint. We also
show that the problem of stabbing a set of disjoint unit squares in $\Rtwo$
with lines of arbitrary directions is W[1]--hard with respect to $k$. Several
generalizations to other types of objects and lines with arbitrary directions
are also presented. Finally, we show that deciding whether a set of unit balls
in $\Rd$ can be stabbed by one line is W[1]--hard with respect to the dimension
$d$.
