I’m a notorious cheapskate, so I buy generics of just about everything – except Q-Tips and Earl Grey tea; for the latter, only Twinings will do. (The inspiration for this thread can be found in the Marketplace, specifically THespos’slovely discount for Dopers on Twining products, which I jumped all over with glee.)
For what products do you insist on the name brand?
Windex. Sony TVs.
Tabasco sauce, Q-tips, and Hebrew National hotdogs (if I’m gonna eat a hotdog, I might as well eat one that tastes good); and I buy booze and beer that I know I’m going to like.
Ketchup - Heinz
Mayonnaise - Hellmans
Peanut Butter - Jif
I have no problem with generics or other brands for pretty much everything else.
Keen Shoes
Merrill Shoes
Sigg water bottles
North Face coats
Patagonia stuff
That’s about it.
Peanut butter: Skippy or Jif. Generic peanut butter is icky.
Canned veggies: LeSeur. We don’t use a lot of canned veggies, but we do love LeSeur’s baby peas, like to make gingered glazed carrots with the LeSeur baby carrots, and my hubby’s fave is their baby peas with pearl onions and mushrooms.
Mayo: Kraft, Duke’s or Hellman’s. Again, mayo? No generics.
Colas: Coke or Pepsi, doesn’t matter; generic flavored sodas are fine, but generic colas are nasty. I’ve never had one that didn’t taste like ass.
Ah, yes. I prefer Nike shoes. And Skippy – or sometimes Jif – peanut butter. We use Starbucks drip coffee at home.
Also, a tiny bit off-topic, while I don’t have a preferred brand, I have become a bed sheet snob. If it ain’t at least 600TC (higher is even better), all-cotton, either pure 'Pima, pure Egyptian, or a blend thereof, it ain’t going on my bed.
Folks, if you’ve never bought high-end sheets because you found them at an impossible-to-pass-up-price, don’t do it! You’ll never be able to buy $30.00 sheets at Target again!
BiC mechanical pencils
Pilot G-2 gel pens
Progresso soups
Cheez-Its (Cheese Nips are gross. Goldfish are fine).
Ricola cough drops (specifically Echinacea Honey Lemon)
It’s technically not a name-brand, but we only get the Kroger generic cheese. I’ve tried generic cheese from the other grocery stores around here, and they just don’t taste right.
Also, Folger’s coffee. It’s actually not my favorite coffee, but it’s the lowest name-brand I’m willing to go to, if that makes sense.
And, Cheerios. I don’t eat them, but MrWhatsit and the little Whatsits do, and the generics just aren’t the same.
I don’t compromise on stain pre-treater for the laundry- it’s Zout or Spray & Wash only.
Dishwasher detergent is another one where I have a very short list of accepted brands- Cascade complete tablets or the electrasol equivalent (Fusion? at any rate, gray with red ball)
Plastic wrap is another one where the cheap versions are notably inferior.
My wife swears by Reynolds Wrap for tin foil, but I’ve never noticed any appreciable difference.
I’m a motor oil snob to an extent- Shell/Pennzoil/Quaker State(brands of same company) or Exxon/Mobil are my 2 brands that I prefer, with Castrol and Havoline being fine if they’re on sale. Never liked Valvoline or house brands.
Hellman’s Mayonnaise
I am the exact opposite. While I like Cheerios just fine, I usually prefer the generic version. The generics tend to be a little rougher in texture and richer in flavor.
The only toilet paper I’ll buy, unless it’s an emergency, is Scott. I HATE the fluffy stuff, and generics are too rough.
My wife says OB tampons.
Joe
This is exactly why I don’t buy high-end sheets. 
Pop Tarts
Nutri Grain cereal bars but I don’t buy them at regular price, I wait until they go on sale and buy a six month supply. The store brands suck.
Motorcraft oil and filters.
Oh and I never compromise on my Yellow Box Cheerios. Not Wheat O’s or Trusted O’s or Fiber O’s or any other kind of O’s…it’s Cheerios. 
Dish detergent and laundry detergent
Carpet cleaning detergent
Toothpaste
Certain breakfast cereals
Peanut butter
I have no problem with store brands and generics for a lot of things, but experience has shown me that the items above really are better from a name-brand manufacturer.
Oh, yeah, dish soap! Dawn only!
My automatic dishwasher tablets I’m not so picky about; whatever’s on sale (but I do buy the tablets, not the powder or liquid).
Listerine - the *proper *kind, which tastes only of eucalyptus and suffering.
Reynold’s aluminum foil.
Ford vehicles.
Levis jeans but only from higher-end stores (low-end stores have low-end Levis and the crotches always tear).
Apple computers (well, I have one non-Apple, but it still has OS X on it anyway).
Aunt Millie’s bread.