I don't believe you can have this automatically happen, natively in Splunk. The user should be able to trigger this with a Ctrl+Click or you can build it into your app with something like sideview_utils (which is a more significant undertaking, albeit rewarding if you're going to build a Splunk app).
I'm using Chrome in Win7 and Ctrl-Clicking elements of search results doesn't open a new tab, nor does shift-clicking open a new window. These mechanisms do work as expected outside of splunk.
Holding down ctrl while clicking on an entry in your search window should open a new window/tab. I just verified that it works in Chrome, Firefox and IE on Windows 7. I should have included this initially, but on a Mac, you hold the Apple button and click to open the link in a new tab. This is a feature of the browser, rather than Splunk, so it can be turned off, if the browser allows it. You can test that it works by clicking on a link from Google, or what have you.
"The user should be able to trigger this with a Ctrl+Click"
What is "this?" To me it looks like ctrl-clicking only starts a new search in the current window, which is undesirable in my situation.