Natural maximization problems in FPT Is there a natural (and hopefully well-known) maximization problem that is known to be in FPT?
For instance, Vertex Cover is in FPT, but it's a minimization problem. 
I'm looking for natural maximization problems that are in FPT. 

Edit (clarification): "I assume you mean a maximization problem that is in FPT when parameterized by the solution size." This is exactly what I meant to ask, as the first comment (by Jan Johannsen) points out.
Here are a few:


Max Cut: Can one color the vertices of an input graph $G$ black and white so that at least $k$ edges go from black to white?
Max Sat: Is there an assignment that satisfies at least $k$
clauses?
Max Leaf: Does $G$ have a spanning tree with at least $k$
leaves?
Longest Path / Cycle: Does $G$ contain a simple path / cycle on at least $k$
vertices? 
3-Set Packing: Given a set family ${\cal F}$ of sets of
size $3$, are there $k$ pairwise disjoint sets in ${\cal F}$?