How can I find out what version of git I'm running?

Question

$ git --version
git version 1.7.3.4

git help and man git both hint at the available arguments you can pass to the command-line tool

If you're using the command-line tools, running git --version should give you the version number.

In a command prompt:

$ git --version

Or even just

git version

Results in something like

git version 1.8.3.msysgit.0

From Gareth's answer:

git help and man git both hint at the available arguments you can pass to the command-line tool

Actually, the git version command finally gets an official help page with Git 2.34 (Q4 2021):

See commit b6d8887 (14 Sep 2021) by Matthias Aßhauer (rimrul).
^{(Merged by Junio C Hamano -- gitster -- in commit 188da7d, 23 Sep 2021)}

documentation: add documentation for 'git version'

^{Signed-off-by: Matthias Aßhauer}

While 'git version'^(man) is probably the least complex git command, it is a non-experimental user-facing builtin command.
As such it should have a help page.

Both git help^(man) and git version can be called as options (--help/--version) that internally get converted to the corresponding command.
Add a small paragraph to Documentation/git.txt describing how these two options interact with each other and link to this help page for the sub-options that --version can take.
Well, currently there is only one sub-option, but that could potentially increase in future versions of Git.

git version now includes in its man page:

git-version(1)

NAME

git-version - Display version information about Git

SYNOPSIS

git version [--build-options]

DESCRIPTION

With no options given, the version of 'git' is printed on the standard output.

Note that git --version is identical to git version because the former is internally converted into the latter.

OPTIONS

--build-options

Include additional information about how git was built for diagnostic purposes.

git now includes in its man page:

This option is internally converted to git version ... and accepts the same options as the git version command.
If --help is also given, it takes precedence over --version.