#PowerShell, 147 bytes

param($a)function z{param($n,$d)ls $n.fullname|%{$f=$_.mode[0]-ne"d";Write-Host(" "*$d*4)"$($_.name)$(("\")[$f])";If(!$f){z $_($d+1)}}}$a;z(gi $a)1

Man, I feel like PS should be able to do something like the bash answer, but I'm not coming up with anything shorter than what I've got here.

Explanation:

param($a)                     # assign first passed parameter to $a
function z{param($n,$d) ... } # declare function z with $n and $d as parameters
ls $n.fullname                # list out contents of directory
|%{ ... }                     # foreach
$f=$_.namde[0]-ne"d"          # if current item is a file, $f=true
Write-Host                    # writes output to the console
(" "*$d*4)                    # multiplies a space by the depth ($d) and 4
"$($_.name)$(("\")[$f])"      # item name + the trailing slash if it is a directory
;if(!$f){z $_($d+1)}          # if it is a directory, recursively call z
$a                            # write first directory to console
z(gi $a)1                     # call z with $a as a directoryinfo object and 1 as the starting depth

PowerShell, 147 bytes

param($a)function z{param($n,$d)ls $n.fullname|%{$f=$_.mode[0]-ne"d";Write-Host(" "*$d*4)"$($_.name)$(("\")[$f])";If(!$f){z $_($d+1)}}}$a;z(gi $a)1

Man, I feel like PS should be able to do something like the bash answer, but I'm not coming up with anything shorter than what I've got here.

Explanation:

param($a)                     # assign first passed parameter to $a
function z{param($n,$d) ... } # declare function z with $n and $d as parameters
ls $n.fullname                # list out contents of directory
|%{ ... }                     # foreach
$f=$_.namde[0]-ne"d"          # if current item is a file, $f=true
Write-Host                    # writes output to the console
(" "*$d*4)                    # multiplies a space by the depth ($d) and 4
"$($_.name)$(("\")[$f])"      # item name + the trailing slash if it is a directory
;if(!$f){z $_($d+1)}          # if it is a directory, recursively call z
$a                            # write first directory to console
z(gi $a)1                     # call z with $a as a directoryinfo object and 1 as the starting depth