If I find a better deal, I take it for most things. On hardware though, I do my research because nothing is worse than getting a shoddy piece of crap.
I do like GOG for my game purchases though. So I guess that can be considered brand loyalty, but it is the only brand I am tentatively loyal to...

I use to be, but not really any longer.
However, I do try to buy American if possible even if it is a little more.
Also, I would think many that are not brand loyal, are in a sense. If their favorite band cuts a new CD they buy it. If so, that is a form of brand loyalty. I am not much of a music guy myself, but I was in the past.
Same with sports teams; if you support one certain team no matter what, that is brand loyalty. I am not a sports fan of any sort so no risk here!
All that to say, since companies, sports players, etc., are not loyal to people I have no impetus to be loyal to them.
All that to say, since companies, sports players, etc., are not loyal to people I have no impetus to be loyal to them.

Wait, loyalty to a product, a business? Something that when it comes down to it is just trying to take your wealth and add it to its own, to line the pockets of some high mucky-mucks?
Uh, nope. Go for the easiest on the wallet, best service, greatest deals.

Not the least. But I tend to go with what I know (via experience) is quality.
If there is a product I favour, and I come across a load of advertisements for it, (internet/Print/TV) I'll even avoid said product (week/month) due to the annoyance they gave me :)

I'm loyal to only companies that I use a lot over time and that give me good service, reliability, and that other category in Conusmer Reports.
For example, I'm loyal to Starbucks. Flame me all you want, but unless if I really really really had to find another place, I'd go to Starbucks for a burnt, overpriced latte just because I'm just so used to it in my area. Or I'm loyal to Mountain Dew (sorry, "Mtn Dew"), and I'm brand loyal to the iPod, but I do have a Zune.
Speaking of brands and how vain they can make you, if you haven't read it already you should read No Logo by Naomi Klein.

After many years of bad experience with AMD/ATI, I'm sticking with Intel & Nvidia all the way.

Damn, now you mention it, I've been with AMD for 6 years now. I still don't mind if my next chipset is intel though.

I agree. I still use a dual core Core 2 Extreme from 2006 and an 8800GTX from the same year. Still no need to upgrade.

I have loyalty to lots of businesses, based mostly on their reputation, past performance and customer service (my favourite chocolate shop, Canon, Pixar, etc.). They will get my repeated (but not exclusive) business.
I think this is sensible; prejudicing yourself in favour of certain brands makes your future choices more simple and less risky. This is usually a good thing, like the OP with his Nike shoes.
I have serious problems with the brand allegiance which most companies are chasing these days, where my choice of brand is no longer a decision based on product merit, but a lifestyle statement that will be assessed by my friends.
When a colleague starts questioning you about why your latest pen purchase wasn't a Mont Blanc, something has seriously gone wrong with brand loyalty.

Word. I think Starbucks and McDonalds really understand branding. It doesn't matter how much I dislike their food, it's still a relieve to see the golden arches in another country and know that I'll be able to order something I can understand.

I am not loyal to anyone.
I buy games on GOG. Then Steam makes ubisoft pack - I buy it there.
I use ATI X1900XTX.
Then nVidia releases GTX280 which is better, I buy that.
I use AMD Athlon64 3000+.
Then Intel releases Core2Duo which is better.I buy that.
Etcetera : ).
But I do tend to prefer one brand over the other, if both offer the same stuff for the same price, my previous experience (=sympathy) decides.