MailTo links do not open Outlook

It sounds like you are not using Internet Explorer as your default browser then or may not have set the mailto protocol in Windows to use Outlook. This is a different settings than having Outlook set as your default mail client in Windows.

Firefox and really old versions of Opera both have an option to override the system default mail client (in your case: Outlook) and link it to a web mail service or another mail application instead.

Chrome, the latest version of Opera and (of course) Internet Explorer respect the default mail client settings which you have configured in Windows.

Firefox

To set Firefox to respect your default mail client settings in Windows again when clicking on a mailto link choose;

Open the Menu by clicking on the “hamburger” icon (3 lines above each other) in the top right corner-> Options-> tab Applications-> click on the “mailto” drop down list and select: Use Microsoft Outlook.

Note: An alternative way to get to the Options dialog is to press ALT+T to open the old Tools menu and then choose Options. Yet another way (as of Firefox version 38) is to type the following in the Address Bar:
about:preferences#applications

Configuring the MailTo protocol in Firefox (click to enlarge).

Opera

As mentioned, really old versions (up to version 12) of Opera had the default for mailto links set to its own Opera Mail client but you could change it back to Outlook in the following way;

Opera menu-> Settings-> Preferences… (CTRL+F12)-> tab Advanced-> section Programs-> select: mailto-> button Edit…-> select: Open with default application.

However, it is really recommended to update to the latest version of Opera instead since these old versions are no longer supported. The latest version of Opera uses the default mailto application that you have set in Windows.

Changing the default mailto application handler to Outlook

Even when you have Outlook set as your default mail client in Windows, it may not have been set as the default handler for the mailto protocol itself.

You can change this in one of the following ways:

Method 1: Windows 8, Windows 7 and Windows Vista

Control Panel-> Programs-> Default Programs-> Set your default programs-> select Outlook (desktop)-> Either use “Set this program as default” to assign Outlook all the defaults it can have or use “Choose defaults for this program” to manually select the MAILTO protocol.

Method 2: Windows 8, Windows 7 and Windows Vista

Control Panel-> Programs-> Default Programs-> Associate a file type or protocol with a program-> scroll down to the protocol list-> select MAILTO-> click the Change program… button in the top right corner to set it to Outlook.

Windows XP

Control Panel (Classis View)-> Internet Options-> tab: Programs-> dropdown list: E-mail-> select Microsoft Outlook from the list.

Control Panel (Category View)-> Network and Internet Connections-> Internet Options-> tab: Programs-> dropdown list: E-mail-> select Microsoft Outlook from the list.

Selecting all the defaults for Outlook 2013 in Windows 8.1 via Method 1.
(click on image for full dialog)