Below is a list of useful Powershell commands that I use day to day – This list will be built upon over time:

Windows Server:

Get a list of running services:
Get-Service | Where-Object {$_.Status -eq "Running"}

Microsoft Exchange Server

Connect to Office 365 Exchange Online:
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
Import-PSSession $Session

Get list of permissions on a users Mailbox Calendar:
get-MailboxFolderPermission -Identity [email protected]:\Calendar

Add a permission onto a users Mailbox Calendar:
Add-MailboxFolderPermission -Identity [email protected]:\calendar -User [email protected] -AccessRights Editor

Office 365 Administration

Connect to Office 365 via Powershell:
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
Import-PSSession $Session
Connect-MsolService -Credential $UserCredential

Other Articles that may interest you:
Powershell Cmdlets to remember for the Microsoft 70-346: Managing Office 365 Identities and Requirements Exam

Powershell Cmdlets to remember for the Microsoft 70-347: Enabling Office 365 Services Exam