Git branch command behaves like 'less'

Not to argue semantics, but the behavior you're getting is the default. That's why you get it when you don't ask for something different. By default, branch (and numerous other Git commands) use a pager when sending output to the terminal.

You can override this default by using the --no-pager option:

git --no-pager branch

Or if you redirect the output to a file, Git should detect that it isn't writing to a terminal and so should not use a pager anyway. (On the other hand, that suggests a scripting use case, in which case you should consider using a plumbing command like git for-each-ref in preference to git branch.)

As other answers pointed out, Git defaults to piping itself into a pager (less by default) for most commands.

An important point, though, is that when the LESS environment variable is unset, Git sets it to FRX, and the consequence is that the user-visible behavior is the same as if the pager was not used when the command's output is short (i.e. if you have only few branches). See man less:

-F or --quit-if-one-screen
Causes less to automatically exit if the entire file can be displayed on the first screen.

-R or --RAW-CONTROL-CHARS
[...]ANSI "color" escape sequences are output in "raw" form.

-X or --no-init
Disables sending the termcap initialization and deinitialization strings to the terminal. This is sometimes desirable if the deinitialization string does something unnecessary, like clearing the screen.

If you get the behavior you describe, you most likely have $LESS set to something else, and unsetting it (unset LESS) would get rid of the issue while keeping the "pager" behavior for long output. Alternatively, you can activate the behavior for while keeping $LESS as-is by adding this to your .gitconfig file:

[core]
    pager = less -FRX

If you really dislike the pager thing, you can deactivate it globally or on a per-command basis (see other answers).

As mentioned in comments to Mark Adelsberger's answer, this was a default behavior change introduced in Git 2.16.

You can turn paged output for git branch back off by default with the pager.branch config setting:

git config --global pager.branch false