Here's a little analogy using shoes instead of tires:
How important are shoes to your feet? 
-Would you wear hiking boots to run a marathon in?
-Would you wear tennis shoes to hike in the snow?
-How about playing football in sandals?
Tires are very important. But since I dont have lots of money laying around, I get a good and a (somewhat) cheap (price-wise) tire, but still a quality tire is best. I can't pay $100+ per tire and then installation, just wont fit the budget. Kuhmos are great for a balance between budget and performace. I've had nothing but good experience with them.
Not only handling, etc... I do a lot of driving on the Taconic State Parkway here in NY. The should register that road as a certified hydroplane testing lab. There's no crown to speak of in the road, and when they built it they put curbs right at the edge of the pavement to make sure the driving surface maintains the maximum amount of water.
And yeah, I'm in the price/value segment, and I'm pretty happy with the Kumho's I picked up...
^^^I disagree. I would much rather have drums all around and really good tires than 14" Brembos and ultra-cheap tires. The car with the best tires will stop far shorter again and again, and have vastly improved handling and acceleration on top of it.
Brakes are very important, but not nearly as much as tires.