On this Exchange TechNet Wiki page is a list of common Exchange 2010 PowerShell cmdlets
Find more common cmdlets in the Exchange 2010 Exchange Management Shell Quick Reference download.

Moving Mailboxes
New-MoveRequest -Identity <user ID> -TargetDatabase "DB01"

Get-MoveRequestStatistics  -Identity <user ID> | ft

View Move Request TechNet Page

User Objects
get-user | sort-object name
get-user | sort-object name -descending
get-user "name" | format-list
get-user | where-object {$_.distinguishedname -ilike '*ou=sales,dc=domain,dc=com'} | Enable-mailbox -database 'servername\databasename'
get-user -filter {(recipienttype - eq 'user') - and (city -eq 'cityname')}

Recipients
enable-mailuser -identity name -externalemailaddress name@domain.com
enable-mailbox "displayname" -database "storagegroup\database"
set-mailbox name -hiddenfromaddresslistsenabled $true/$false -prohibitsendquota unlimited -primarysmtpaddress "name@domain.com"
new-mailbox -userprincipalname "name@domain.com" -alias name -database "name" -name name -organizationalunit name -Firstname name -lastname name -displayname "first last"
get-mailbox -database "database"
move-mailbox name -targetdatabase "server\database"
add-mailboxpermission name -user name -accessrights fullaccess
new-distributiongroup -name "name" -organizationalunit "name" -samacccountname "name" -type "security"
set-distributiongroup name -hiddenfromaddresslist $true
new-mailcontact -name "display name" -externalsmtpaddress "name@domain.com" -organizationalunit contractors
set-contact "name" -company "name"
enable-mailcontact "name" -externalemailaddress "name@domain.com"
get-mailboxstatistics "username" | format-list
get-mailboxstatistics -server "name" | format-list
get-mailboxstatistics -server "name" | sort-object -property totalitemsize

Meeting Resources
new-mailbox -userprincipalname "name@domain.com" -alias name -database "name" -name name -organizationalunit name -displayname "name" -room/-equipment
set-mailboxcalendarsettings name -automateProcessings autoaccept
set-mailboxcalendarsettings name -resourcedelegate name

Mail Store
get-mailboxdatabase -server name | set-mailboxdatabase -issuewarningquota 100mb -prohibitsendquota 100mb
mount-database databasename
dismount-database databasename
new-storagegroup name -server name
new-mailboxdatabase name -storagegroup name

Public Folders
new-publicfolder name -server name
set-publicfolder \name -replicas "server\database","server2\database2"
get-publicfolder \name
set-publicfolderdatabase "server\database" -usecustomreferralserverlist $true/$false -publicfolderreferralserverlist $null
get-publicfolderstatistics
enable-mailpublicfolder -i "\foldername"

Transport
new-accepteddomain -name "name" -domainname name.domain.com -domaintype authoritative
new-emailaddresspolicy -name "name" -includedrecipients allrecipients -conditionaldepartment "departmentname" -enabledemailaddresstemplate: "SMTP:%g.%s@mkt.adatum.com","%g.%s@adatum.com"
set-emailaddresspolicy "name" -Priority #
get-emailaddresspolicy
update-emailaddresspolicy "policyname"
get-queue
freeze-queue
unfreeze-queue
get-transportserver | get-messagetrackinglog -messagesubject "subject" -Sender "sender address" -Recipients "Recipients"

Edge Transport
new-edgesubscription -filename "filelocation"
start-edgesynchronization

Address List
new-addresslist -name "listname" -conditionaldepartment "departmentname" -includedrecipients mailboxusers -container "containername"
update-addresslist "listname"

Testing
test-mailflow
test-owaconnectivity
test-mapiconnectivity
test-servicehealth
test-systemhealth

Autodiscover
new-outlookprovider
get-outlookprovider
set-outlookprovider exch -server "servername"
remove-outlookprovider
new-autodiscovervirtualdirectory
get-autodiscovervirtualdirectory
set-autodiscovervirtualdirectory -externalurl URL -internalurl URL -path "location"

Out of Office
set-mailbox name -externaloofoptions internalonly/external

List initially from: http://www.experts-exchange.com/Microsoft/Windows_Security/Q_23660234.html