How to uninstall the "Microsoft Advertising SDK" Visual Studio extension?

Run the following from an elevated Powershell prompt:

gwmi Win32_Product -Filter "Name LIKE 'Microsoft Advertising%'"

And it should show the culprits:

IdentifyingNumber : {6AB13C21-C3EC-46E1-8009-6FD5EBEE515B}
Name              : Microsoft Advertising SDK for Windows 8.1 - ENU
Vendor            : Microsoft Corporation
Version           : 8.1.30809.0
Caption           : Microsoft Advertising SDK for Windows 8.1 - ENU

IdentifyingNumber : {6AC81125-8485-463D-9352-3F35A2508C11}
Name              : Microsoft Advertising SDK for Windows Phone 8.1 XAML - ENU
Vendor            : Microsoft Corporation
Version           : 8.1.40427.0
Caption           : Microsoft Advertising SDK for Windows Phone 8.1 XAML - ENU

IdentifyingNumber : {5C87A4DB-31C7-465E-9356-71B485B69EC8}
Name              : Microsoft Advertising SDK for Windows Phone - ENU
Vendor            : Microsoft Corporation
Version           : 6.2.960.0
Caption           : Microsoft Advertising SDK for Windows Phone - ENU

IdentifyingNumber : {EBD9DB6D-180B-4C59-9622-B75CC4B32C94}
Name              : Microsoft Advertising Service Extension for Visual Studio
Vendor            : Microsoft Corporation
Version           : 12.0.40402.0
Caption           : Microsoft Advertising Service Extension for Visual Studio

Then to actually uninstall add | foreach { $_.Uninstall() } to the command like so:

gwmi Win32_Product -Filter "Name LIKE 'Microsoft Advertising%'" | foreach { $_.Uninstall() }

Which should display for each one:

__GENUS          : 2
__CLASS          : __PARAMETERS
__SUPERCLASS     : 
__DYNASTY        : __PARAMETERS
__RELPATH        : 
__PROPERTY_COUNT : 1
__DERIVATION     : {}
__SERVER         : 
__NAMESPACE      : 
__PATH           : 
ReturnValue      : 0
PSComputerName   : 

The important thing to look for is ReturnValue : 0 which means success. If you get ReturnValue : 1603 it likely means your Powershell prompt wasn't elevated (running as admin). (Full list of ReturnValues documented here)

Total Uninstaller is a simple UI tool for removing "Microsoft Advertising SDK" and similar sw.

The PowerShell answer given by Duncan Smith above is great. However, as an alternative, in the case of VS2013, if you have the iso image for the Visual Studio installation, if you navigate to the packages\AdsSDK10 folder, you will find two files,

MSAdvertisingServiceExtension.msi
Win8_1AdSDK.msi

If you right click on these, you can choose the uninstall option, and this will remove the pubCenter Integration and the Advertising SDK for Windows 8.1

For this, and all other bloatware that comes with VS 2012 and 2013 (and 2015 - I highly doubt that the current trend will ever revert back to the advanced customization options of 2010), simply install Revo Uninstaller (has a fully functional free trial), and enable "Show system components" in its options, and voila - simple as that.

Some integrated components may refuse to be removed - but if you are absolutely sure about it, just right click on them and select "Forced Uninstall", and that's it. The most offending ones, especially the extensions with their "Uninstall" button disabled (grayed out) in VS, are perfectly safe to remove - they even warn if something else depends on them, so no worries there either.