I'd like to run CAT6 cable between 3 rooms which are separated by concrete walls. What are my options? I'm looking for the least intrusive way.
Concrete walls typically have conduits where all wiring passes (edit: as pointed out by @alx9r, this might not always be the case. Sometimes wiring is cast directly into the concrete). This allows you to add additional wires to the same conduits, but doesn't help if you need to pass a wire between two places that don't have a conduit already in the wall.
Whether or not you can use the existing conduits is both a matter of convenience (are there existing conduits from and to the place you want to run the Ethernet cabling) and of wiring code - is it allowed to run Ethernet (low voltage) cabling along side other cables - high voltage (110/220 V), phone lines, TV coaxial cables, etc.
If there are no existing conduits you can use, you'd need to consider several options (all pictures from Google Images):
Run the cable along the walls, often by the skirting boards. The cable can be attached with clips to the wall. This method is easiest, cheapest and fastest, but people often don't like cables running visibly around the house and if the cables aren't properly secured they might be a tripping hazard.
Run the cables in plastic channels that are attached to the walls. This is similar to number 1, only that the channels help hold the cable better and are probably more aesthetic.
Run new conduits in the wall. This is done by carving a channel in the wall (called "wall chasing"), placing a plastic conduit in the channel, mortaring the conduit in place and patching up the channel on top of the conduit. As can be imagined, this is hard work (especially for long distances), very dirty (especially if grinding disc cutters are used to score the channel) and must be done carefully to avoid hitting other cables and pipes already in the wall. However, this will give the best aesthetic result.
If a conduit is used, fishing the new cable through the conduit is done either using preexisting cables in the conduit or with a fish tape. The new cable is attached to the preexisting cable or the fist tape (after pushing the fish tape through the conduit to the other side) and then pulled until the new cable is fully in the conduit. From my experience, if you have cables already in the conduit, it is much easier to pull them completely out and then fish the entire bundle (old cable/cables together with new Ethernet cable) back into the conduit.
Finally, Cat6 doesn't give that much of a difference in the common house over Cat5e - the extra shielding is useful with lots of cables running close together and for long distances. For home use spans are usually much shorter than the maximum 100 meters defined for Ethernet and there are only a few cables running side by side. However, Cat6 is much stiffer than Cat5e, making it quite challenging to fish it through conduits.
An network alternative to ethernet or powerline is MoCA using the cable coax that already exists in many homes. Also you could go wireless A1C modems, faster than G or N. Ethernet is the best option but MOCA works well and is fast enough to stream videos/movies. Powerline is great for data and networking, but interference can occur for streaming movies.
I faced exactly the same problem, and solved it through a PowerLine Adapter system, based on 500mbs/1Gb Ethernet port powerline units, and heavy encryption - all centrally and remotely controlled. Home power meters are probably preventing packet hopping what additionnally prevents infiltration. This option is more expensive but much more comfortable and certainly the least intrusive.