user10024: Adafruit has this wonderful product: http://www.adafruit.com/products/85

What are these actually called? I've looked all over the place in Mouser and DigiKey and can't find them (now, granted, it's impossible to find anything in DigiKey since they discontinued their printed catalog, but I'm digressing...)
They are great for putting other things that are on breakout boards on a tightly-packed breadboard and still be able to attach probes.
Also, sometimes, the board you are trying to attach is this:
As you can see, there is a dip switch blocking the 8-pin header. This is fine for its final resting place (on a board with a socket), but putting it on a breadboard is a bit of a pain. I have quite a few of those, so even though the aforementioned adafruit part is pretty cheap and I could get a bunch, I'd rather know what the real part is called so I can get the sizes I need.
PS: In case you are wondering, and you like old-style nixie tubes, that's http://www.tayloredge.com/storefront/SmartNixie/DataSheets/Datasheet_SmartNixie.pdf.)

user10175: If you are already ordering from Digi-Key, they do carry the same set of stackable headers from Adafruit.  It's just a bit hidden in an accessories family.  Otherwise it looks like Samtec is the only company Digikey carries that makes this style of connector.  Some dual-row long tail headers can be found using the term stackthrough, but this is mostly used in conjunction with PC104 connectors. 

user10187: You can find stackable headers on eBay (ie. 141063314400 , 191576393028 , 271841707614). Futurlec also sell them pretty cheap - about half-way down the page.

user4143: They're actually called "Wire-Wrap Headers" and they pre-date the Arduino probably by at least 50 years or so.
They used to be used to create circuits between chips and components by wrapping wire around the pins and routing it to other connectors:

They have since been adopted as stackable headers on boards like the Arduino shields.
Being such old technology not many people make them any more, though thanks to their popularity on things like the Arduino they are starting to appear more and more from normal electronics supply companies.

user3917: A Digikey.com search for samtec SSQ includes numerous longtail stackable headers (as well as some shorttail, or non-stackable).  However, looking at Digikey's prices suggests to me that adafruit.com's price is a bargain unless you are purchasing thousands of pieces.
Also see an arduino.cc thread on this topic.

10024: <p>Adafruit has this wonderful product: <a href="http://www.adafruit.com/products/85" rel="nofollow noreferrer">http://www.adafruit.com/products/85</a></p>

<p><img src="https://i.stack.imgur.com/caRKC.jpg" alt="enter image description here"></p>

<p>What are these actually called? I've looked all over the place in Mouser and DigiKey and can't find them (now, granted, it's impossible to find anything in DigiKey since they discontinued their printed catalog, but I'm digressing...)</p>

<p>They are great for putting other things that are on breakout boards on a tightly-packed breadboard and still be able to attach probes.</p>

<p>Also, sometimes, the board you are trying to attach is this:<img src="https://i.stack.imgur.com/stwEE.jpg" alt="TaylorEdge Smartnixie board"></p>

<p>As you can see, there is a dip switch blocking the 8-pin header. This is fine for its final resting place (on a board with a socket), but putting it on a breadboard is a bit of a pain. I have quite a few of those, so even though the aforementioned adafruit part is pretty cheap and I could get a bunch, I'd rather know what the real part is called so I can get the sizes I need.</p>

<p>PS: In case you are wondering, and you like old-style nixie tubes, that's <a href="http://www.tayloredge.com/storefront/SmartNixie/DataSheets/Datasheet_SmartNixie.pdf" rel="nofollow noreferrer">http://www.tayloredge.com/storefront/SmartNixie/DataSheets/Datasheet_SmartNixie.pdf</a>.)</p>
 10175: <p>If you are already ordering from Digi-Key, they do carry the <a href="http://www.digikey.com/product-detail/en/85/1528-1074-ND/5154649" rel="nofollow">same set of stackable headers</a> from Adafruit.  It's just a bit hidden in an accessories family.  Otherwise it looks like Samtec is the only company Digikey carries that makes this style of connector.  Some dual-row long tail headers can be found using the term <a href="http://www.digikey.com/product-search/en?keywords=STACKTHROUGH%20&amp;stock=1" rel="nofollow">stackthrough</a>, but this is mostly used in conjunction with PC104 connectors. </p>
 10187: <p>You can find stackable headers on eBay (ie. 141063314400 , 191576393028 , 271841707614). <a href="http://www.futurlec.com.au/ConnHead.jsp" rel="nofollow">Futurlec</a> also sell them pretty cheap - about half-way down the page.</p>
 4143: <p>They're actually called "Wire-Wrap Headers" and they pre-date the Arduino probably by at least 50 years or so.</p>

<p>They used to be used to create circuits between chips and components by wrapping wire around the pins and routing it to other connectors:</p>

<p><img src="https://i.stack.imgur.com/JxfcL.jpg" alt="enter image description here"></p>

<p>They have since been adopted as stackable headers on boards like the Arduino shields.</p>

<p>Being such old technology not many people make them any more, though thanks to their popularity on things like the Arduino they are starting to appear more and more from normal electronics supply companies.</p>
 3917: <p>A <a href="http://www.digikey.com/product-search/en/connectors-interconnects/rectangular-connectors-headers-receptacles-female-sockets/1442548?k=%20SSQ%20samtec" rel="nofollow">Digikey.com search for <code>samtec SSQ</code></a> includes numerous longtail stackable headers (as well as some shorttail, or non-stackable).  However, looking at Digikey's prices suggests to me that <a href="http://www.adafruit.com/products/85" rel="nofollow">adafruit.com's price</a> is a bargain unless you are purchasing thousands of pieces.</p>

<p>Also see <a href="http://forum.arduino.cc/index.php?topic=23857.0" rel="nofollow">an arduino.cc thread</a> on this topic.</p>
