There is no such thing as "incoming commits" users commit locally and push them. I would open up gitx or gitk(that comes with git) and check out what the repos looks like... I think that will give you a clear view.
use: gitk --all to see.
You may want to examine the difference between two repositories. Assumed you have a local branch 'master' and a remote-tracking branch 'origin/master', where other people commit their code, you can get different stats about the differences of the two branches:
git diff --summary master origin/master
git diff --stat master origin/master
git diff --numstat master origin/master
git diff --dirstat master origin/master
git diff --shortstat master origin/master
git diff --name-only master origin/master
git diff master origin/master
incoming isn't quite a direct mapping in git because you can (and I often do) have multiple repos you're pulling from, and each repo has multiple branches.
If there were an equivalent of hg's incoming command, it'd probably be this:
git fetch && git log ..origin/master
That is, "go grab all of the stuff from the upstream, and then compare my current branch against the upstream master branch."
Similarly, outgoing would be this:
git fetch && git log origin/master..
In practice, I just type those manually (even though I created an alias for one of them) because it's easy to have lots of local branches tracking and being tracked by lots of remote branches and have no trouble keeping it together.
You may also be interested in git whatchanged which gives a good overview of changes that have been made in some range of commits.
If you want to review what you're about to pull, do a git fetch first, which only updates local tracking branches for the remote repository (and not any of your branches), and then use any command that shows you the new commits that you're about to pull. For example:
git whatchanged ..origin
This is shorthand for showing the commits between "the common ancestor of wherever I am now and origin" through "origin".
when someone tells you to pull, they will give you the repo URL and a branch (default being master)
I'd just do
git fetch URL branch
followed by one (in decreasing order of preference):
# note 3 dots in next 3 commands
gitk HEAD...FETCH_HEAD
# shows all commits on both sides since the "fork" point
gitk --cherry-pick HEAD...FETCH_HEAD
# as above but skips identical patches so you really see the differences
git log --graph --boundary --left-right --cherry-pick HEAD...FETCH_HEAD
# I have a nice alias for this; it's the text mode eqvt of the above
I also use "tig" sometimes, but this specific usecase (seeing both sides) is not well served by tig.
However, if you bring it down to two dots (which may match your actual question more closely, though I still prefer the 3 dot versions), you can do
tig HEAD..FETCH_HEAD