Takedowns and throws for MMA and No-Gi Grappling are a huge part of the overall picture. They are a must, especially if you are a submission monster on the ground.
For MMA there is no question that you need to have at least 3 or 4 techniques that you have mastered. There is just no way that you can excersize your ground skills if you cannot take your opponent down to the ground.
As far as Wrestling is concerned I believe that Greco Roman Wrestling body locks and throws are the best for MMA. The single & double legs of Freestyle Wrestling are great and you may be able to pull one off if timed right. But at the same time in the words of Rickson Gracie "they're too risky."
It is way too easy when shooting in to dive into the knee or foot of a good striker. Better to close the distance, lock 'em up and then take 'em down.
For grappling tournaments single and double leg take downs are a little bit safer. You must protect your neck from the Guillotine!
Judo techniques can be modified for no-gi grappling and MMA. They are proving to be very effective in MMA. The reason that they are so effective is that they work off of different principles and angles than Wrestling throws.
You will have to setup the Judo throws a little differently without the gi and use overhooks and underhooks instead of the usual grips but once you have your no-gi technique down you will be taking your opponents down at will.