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As per the Implementation guide for CRM 2013 (www.microsoft.com/.../details.aspx), Windows 8.1 has not been tested and isn’t fully supported with this release of Microsoft Dynamics CRM 2013.
Still CRM for Outlook client 2013 would work provided you have deleted the cache and cookies on IE and have added the CRM sites URL (*.dynamics.com) in the trusted sites and in Compatibility view settings in IE. (xrmcubed.com/dynamics-crm-2013-post-upgrade-tips). This should help configuring CRM for Outlook client 2013.
Sadly suggested solution fails. Implementing suggestion prevents browser log on. Thankfully removing IE compatibility setting re-enables browser Dynamics CRM connection.Erratic IE behaviour when implementing solution implies possible reason for Outlook being unable to connect.
As the Implementation guide for CRM 2013 suggests, "Windows 8.1 has not been tested and isn’t fully supported with this release of Microsoft Dynamics CRM 2013." This should be officially declared as supported maybe in the coming Rollup updates for CRM 2013.
The above response illustrates Microsoft inability to turn around their diminishing market attractiveness. Yet again product releases are released with known bugs and most of the time end users are blamed or at least the inference is end users are at fault. Competitors will win if this strategy continues. Its simply customers want solutions that will unquestionably do what it says it will do every time. At the very least admit which products won't function and provide a time line for when the product will function. Proactive approach avoids disappointment and lost sales. Having spent many, many hours researching solutions only to discover my time has been totally wasted disgusts me.
I note your answer sadly doesn't resolve the issue. Customers expect the product to do what it says it will do. If a product doesn't why would a customer want to purchase? Competitors will grab market share if this sort of problem is allowed to continue.
Open Explorer (browser) use Bing homepage to log out of Windows 8 Live ID sign in (if different to your MS Dynamics CRM Windows Live ID sign in). Delete browser history, cache etc. (i.e. select all & delete). If you have MS Dynamics Outlook Client 2011 installed use Control Panel to uninstall this version.
Next download MS Dynamics CRM Outlook client 2013 click here and install. After installation reboot and you should find MS Dynamics Outlook client works perfectly.