Contains process ID of the current hosting process.

PS C:\> $pid
26080

$true and $false are two variables that represent logical TRUE and FALSE.

Note that you have to specify the dollar sign as the first character (which is different from C#).

$boolExpr = "abc".Length -eq 3 # length of "abc" is 3, hence $boolExpr will be True
if($boolExpr -eq $true){
    "Length is 3"
}
# result will be "Length is 3" 
$boolExpr -ne $true
#result will be False

Notice that when you use boolean true/false in your code you write $true or $false, but when Powershell returns a boolean, it looks like True or False

$null is used to represent absent or undefined value.
$null can be used as an empty placeholder for empty value in arrays:

PS C:\> $array = 1, "string", $null
PS C:\> $array.Count
3

When we use the same array as the source for ForEach-Object, it will process all three items (including $null):

PS C:\> $array | ForEach-Object {"Hello"}
Hello
Hello
Hello

Be careful! This means that ForEach-Object WILL process even $null all by itself:

PS C:\> $null | ForEach-Object {"Hello"} # THIS WILL DO ONE ITERATION !!!
Hello

Which is very unexpected result if you compare it to classic foreach loop:

PS C:\> foreach($i in $null) {"Hello"} # THIS WILL DO NO ITERATION
PS C:\>

Variable called Output Field Separator contains string value that is used when converting an array to a string. By default $OFS = " " (a space), but it can be changed:

PS C:\> $array = 1,2,3
PS C:\> "$array" # default OFS will be used
1 2 3
PS C:\> $OFS = ",." # we change OFS to comma and dot
PS C:\> "$array"
1,.2,.3

Contains the object/item currently being processed by the pipeline.

PS C:\> 1..5 | % { Write-Host "The current item is $_" }
The current item is 1
The current item is 2
The current item is 3
The current item is 4
The current item is 5

$PSItem and $_ are identical and can be used interchangeably, but $_ is by far the most commonly used.

Contains status of the last operation. When there is no error, it is set to True:

PS C:\> Write-Host "Hello"
Hello
PS C:\> $?
True

If there is some error, it is set to False:

PS C:\> wrt-host
wrt-host : The term 'wrt-host' is not recognized as the name of a cmdlet, function, script file, or operable program.
Check the spelling of the name, or if a path was included, verify that the path is correct and try again.
At line:1 char:1
+ wrt-host
+ ~~~~~~~~
    + CategoryInfo          : ObjectNotFound: (wrt-host:String) [], CommandNotFoundException
    + FullyQualifiedErrorId : CommandNotFoundException

PS C:\> $?
False

Array of most recent error objects. The first one in the array is the most recent one:

PS C:\> throw "Error" # resulting output will be in red font
Error
At line:1 char:1
+ throw "Error"
+ ~~~~~~~~~~~~~
    + CategoryInfo          : OperationStopped: (Error:String) [], RuntimeException
    + FullyQualifiedErrorId : Error

PS C:\> $error[0] # resulting output will be normal string (not red    )
Error
At line:1 char:1
+ throw "Error"
+ ~~~~~~~~~~~~~
    + CategoryInfo          : OperationStopped: (Error:String) [], RuntimeException
    + FullyQualifiedErrorId : Error

Usage hints: When using the $error variable in a format cmdlet (e.g. format-list), be aware to use the -Force switch. Otherwise the format cmdlet is going to output the $errorcontents in above shown manner.

Error entries can be removed via e.g. $Error.Remove($Error[0]).