Speakers least affected by room acoustics

The advice that most mirrors my experience comes from audiotroy.   If someone come to me asking me to build a speaker for them and they had a lot of boundry room issues.  I would have recommended one of two.  One was nailed above.  An MTM with a rug covering as much of the floor possible in front of the speakers.  Next alternative would be a speaker with a wide front baffle.  
When we build speakers, we use Baffle step compensation to counteract the effects of the sound that shoots around the cabinet.  The wider the cabinet front the less or no compensation is needed.  With a wide front baffle,  it helps keep all drivers firing in the direction the speaker is facing and stops midrange reflections. Still add the rug to the floor to help floor reflections. I then would add to get a sealed box woofer or a front firing port in this case.  Drape as much of the rear wall as possible.  You should be able to pull in some fairly solid results. 

corner loaded speakers like audio note or klipsch can work well with most any room provided it is big enough and you have the freedom to make it work with respect to room layout and furnishings.  

The living rooms (my main listening rooms) in both my previous house and my current house have very high ceilings - 16 feet. I did not have a ceiling echo in either room. The current room is 24 x 14 with speakers on the long wall. All hard surfaces with parallel walls, ceilings, and floors and no treatments - not even an area rug. If I were you, I would speak to a couple of manufacturers such as Sean from Zu and Duke from Audiokinesis.

There are things one can do to "treat" a room that is compatible with normal room decor.  As Shadorne mentioned, start with a thick carpet, or at least a large rug.  This will reduce the slap echo of sound bouncing back and forth between the ceiling and the floor.  If you have a lot of bare walls, put a decorative wall hanging or oriental carpet on the walls.  Book cases or anything else along the wall will also act to break up reflections.

Listening in the nearfield also helps to reduce the effect of the room because a higher percentage of the sound you hear will be coming directly from the speaker.  This requires that the speaker be reasonably balanced for such listening (speakers sound much brighter when listening close up, so not too bright speakers will help).

The use of tall dipole speakers is also a good idea if you can meet the requirement of locating the speaker well off the back wall (about 4 feet or more is needed).  The height of such speakers means they do not radiate as much energy upward, and because they are dipoles, the front and back signals are out of phase and tend to cancel at the sides; the sound is more concentrated within the area between the speakers.

In rooms that are really challenging, and where placement options are limited, a speaker designed to be very flexible in placement can be a big plus.  For example, I've heard Gradient Revolutions used in some really difficult situations and they sounded quite good.

No matter how bad a room seems to be, there are usually setups that will work.  The challenge is finding them.  It can take quite a bit of experimentation and patience to find the right spot.  This is particularly the case because moving one speaker one inch can make a big difference if the speaker is sitting in or near a node (a place where major reflections are either reinforcing or cancelling a frequency).  I would suggest googling the "Sumiko Method" of speaker setup; it is quite useful with tricky rooms.

Good luck.

To the original poster:
* floor standing, or bookshelfs on a stand and how high is the tweeter/HF driver off the floor
* how close are they to any other room boundaries
* is there a big screen TV between them (audio/video system?)
* is it a high ceiling, or vaulted one and if vaulted, are the speakers under the low, or high side
* dome tweeter, or full-range driver (size of sweet spot)
* is your seating position at, or away from a wall/window...and how far back
* how wide are the speakers apart
* is there a window behind your head
* is your carpet Berber, or thicker...or is it wood floors
* is your listening spot a fully upholstered chair and if you scratch your fingernails on it, is it noisy

The point, is that everything makes a difference. Without lifting a finger for any room mods, moving the speakers further into the room -- closer to you -- and using a spacing of no more than 8', tweeter center to center, will help. Toeing them in so you're directly on axis with the tweeter will also lessen the echo effect. The more you're in the direct soundfield (the nearfield as some have mentioned), the less you're affected by the echo. Notice I said you and not your speakers. Do a bit of research on HRTF and you'll understand why.

So we have HRTF, room impulse and frequency response, potential phase shift of a signal from the electronics and a persnicketty wife. Better pick up a pair of cans. :-D