But the card also comes with the negative perception that it's not all that usable, as many retailers don't accept it.
So for those of us who have an American Express card lurking in their wallet, or who are thinking about getting one, is this something we should be worried about, or are those claims exaggerated?
Should we worry?
The good news for current or potential American Express holders is that the number of retailers accepting the card is growing.
The big supermarkets - Asda, Sainsbury's, Tesco and Waitrose - accept American Express, as do plenty of other big retailers like Boots, John Lewis and Marks & Spencer.
Even, since March 2012, Poundland. With their name, reputation and business model - based on tight margins - it would be reasonable to expect them not to accept the card - and yet they do.
But still, American Express's reputation as somehow exclusive persists.
Lloyds and Virgin Atlantic even offer reward deals with two credit cards - an American Express and a standard Visa - so customers can continue to collect rewards, albeit at a lower rate, when shopping in places that don't take American Express.
Someone must be rejecting these cards.
Who doesn't accept it
At the time of writing, these are some of the big high street retailers who don't accept American Express cards in store:
Note that while the traditional UK supermarkets may accept Amex, discount grocers Aldi and Lidl don't - which we might expect, given their cost-cutting ethos.
What makes things more confusing is that some of the big name retailers who accept Amex in their shops, don't accept it in their online stores. Both Ikea and H&M operate this split policy.
Overall, however, we found that most big high street names do take American Express - and if they do in store, they also accept it online.
But what about smaller retailers, who usually have to operate on tighter margins. Would they be less likely to take the cards?
To find out, we polled a sample of 15 independent businesses - five hotels, five restaurants and five bookshops - from across the UK and found that, no matter the type of business, about half were willing to accept American Express transactions.
On first glance, a 50% chance that a business will accept our payment method isn't great odds, which could be where the bad reputation is coming from.
We've also noticed that the vast majority of local councils don't accept American Express for any payment of council tax or charges such as parking tickets.
If for some reason we end up dealing with a charge from a council other than our own, it's possible to track down information about accepted payment methods online - a good starting point is DirectGov's list of local authorities, available here.
In our research we also noticed that it seems to be fairly common for other big institutions such as universities to decline American Express, so if this is likely to be relevant to you, it's worth checking before application.
There's one more group of businesses that we suspect may contribute towards the reputation Amex have for not being widely accepted - and that's the pay TV / internet service providers.
Not one of the biggest providers - BT, Sky, TalkTalk, Virgin or Plusnet - accepts Amex.
As many of us will pay our bills by direct debit, this might not seem all that surprising. But all of them recognise the need for payment by credit card as an option to cover high one-off costs such as setup fees and upfront service payments - they just don't allow them to be made with Amex.
In contrast, the four big mobile operators all accept Amex. Again, for monthly bills they all stress a preference for payment via direct debit - it's cheaper for everyone - but should payment by credit card be necessary American Express cards are welcome.
Why don't organisations like American Express?
There's one simple reason behind much of the reluctance to accept Amex: much higher transaction charges than Visa and Mastercard.
Every time someone makes a payment using a card, the retailer must pay a percentage of the transaction amount. That's why some smaller retailers will have a minimum spend amount for those wanting to use plastic.
Previously these fees ranged from just under 1% to as much as 3% of the transaction value - and in the case of American Express cards, they were up to twice as much as with other cards.
Since December 2015, the fee for transactions involving Visa or Mastercard credit cards within the EU has been limited to a maximum of 0.3% - but many American Express cards are exempt from this cap.
These higher processing fees are a particular issue for councils and educational facilities, where every penny counts - so they don't accept any card with the Amex symbol, exempt or not.
Why do they charge more?
American Express can afford to charge so much more because people with their cards tend to be big spenders.
In the UK at least, anyone with an American Express card has an excellent credit history and will typically have a high income.
Retailers who refuse to take American Express cards are potentially turning away customers who can often spend more than the average customer - just the sort of person whose business they would otherwise be clamouring for.
In addition, the cards themselves encourage holders to spend as much as possible through points schemes like Starwoods, Avios and other airline loyalty schemes, or a percentage of each purchase back as cash back.
Does it matter?
We think the reputation American Express have for being unusable in the UK is a little unfair: although many places don't accept their cards many, many more do.
What's more, American Express cards are only ever available as credit or charge cards - products that people have in addition to their main accounts - so almost everyone with an American Express card will also have either a Visa or Maestro debit card.
That means American Express cardholders - unlike people given Visa Electron cards, for example - aren't likely to find themselves in the position of not having an alternative method of payment.
Of course, if you spend half your life in B&Q you might feel differently.