I stumbled over a neat tool call apt-rdepends today. It can list forward and reverse dependencies as well as generate dot graphs from that. Here are two little examples. Recursive forward dependency lookup of package git-arch as graph:

apt-rdepends - -dotty git-arch | dot -Tpng > git_deps.png

The output looks like this:

Non-recursive reverse dependency lookup of package nano :

$ apt-rdepends –-reverse –-follow=nano nano
Reading package lists… Done
Building dependency tree
Reading state information… Done
nano
Reverse Depends: junior-writing (1.5)
Reverse Depends: mindi (2.22-1ubuntu1)
Reverse Depends: ubuntu-standard (1.79)