i should say YES. BUt... is because there is no other with this popularity/time as FLASH. And is the "only" option outside, i mean, big sites use it as a default tool, for basic stuff as video, music players, banners and stuff. It's solid and have been growing a lot since AS 2 and 3. And for vector animations it's pretty good and simple.
But you have to considerate this...... basically IT SUX a lot... still have so many problems to handle the memory and since it's linked to a browser will not powerfull as it should be. It's a shame because is a powerfull tool but is mismanaged in my opinion. A better options for videogames (with best performance) is the shockwave but is a forget tool. ""Not much"" ppl use it. But it handle a loooot better the elements and dont feel rusty as flash in the graphic part.
In you case, if you want to develop games. There is a HUGE (really really huge) background of GOOD games made in flash. So is a good tool for that. if you dont have much exprience with it will take a bit for you to dev games, because flash is a bit tricky.
I have been using flash since 2000 and doing graphics/animation/sounds for flash games since 2003, so if your goal is to develop games and earn money with. G0G0G0G0