Starting with Git 1.7.0, there is a special syntax that allows you to generically refer to the upstream branch: @{u} or @{upstream}.
To mimic hg incoming:
git log ..@{u}
To mimic hg outgoing:
git log @{u}..
I use the following incoming and outgoing aliases to make the above easier to use:
git config --global alias.incoming '!git remote update -p; git log ..@{u}'
git config --global alias.outgoing 'log @{u}..'