Not a giant physical solid shell around a star, but millions of separate
colonies built around a sun. They wouldn't need to grab all of the
sunlight to get what they require, but there would be enough habitats
to notably dim the star from a distance as well as radiating their own
waste heat. Imagine lots of O'Neil space colonies.

I have been partial to this type of Dyson Shell for a while now, in no
small part because it looks beyond the organic stage of intelligent life:

http://www.aeiveos.com:8080/%7Ebradbury/MatrioshkaBrains/index.html

I also have trouble imagining beings at our level of development being
able to build and maintain a Dyson Shell (Type 2, the solid sphere
version). More computing power and greater overall knowledge would
be required in my opinion.

One of the most impressive and potentially frightening things about a
Dyson Swarm is the ability for it to become what is called the Nicoll-
Dyson Beam:

http://eg.orionsarm.com/xcms.php?r=oaeg-view-article&egart_uid=48fe49fe47202

Apparently a Dyson Swarm’s outer layers can be turned into a very
powerful phased array laser beam. This beam could be used to send
solar sail craft at relativistic speeds across the galaxy. It could also
be used to destroy planet-sized targets many light years from the
Dyson Swarm. Another answer to Fermi's Paradox as Kardashev Type 2
civilizations bump off potential competition as they find them?

By the way, James Nicoll says the first we would know that Earth is
being hit by a Nicoll-Dyson Beam is when our planet's oceans start to boil.

Dyson Shells pale in comparison to this idea, however - a multilayer
structure called a SupraSelf that is 1.2 light years across:

http://www.paulbirch.net/CustomPlanets.html

Then there is the Dyson Galaxy concept....

By the way, if we were inside a Kardashev Type 3 society, which would
basically encompass the Milky Way galaxy, would we even know it?