According to Tim Cook, who spoke at the WDJ.D conference, Apple Pay is already more successful than all of the other "contactless" payment services combined after only a week. To put that in numbers, Apple's CEO said that Apple Pay processed more than 1 million credit/debit card transactions in just three days.
It seems Apple Pay is already highly successful, despite the fact that some major retailers in the US have refused to use it. CVS and Rite Aid have even instructed stores to disable NFC in their registers so people can't perform Apple Pay transactions anymore. This has the side effect that Google Wallet or any other sort of NFC-based payments system also won't work anymore. Walmart has also refused to accept Apple Pay.
The main reason these companies are opposing Apple Pay is because they are all part of the Merchant Customer Exchange (MCX) consortium, which is working on its own mobile wallet solution called CurrentC that is currently available for Android and iOS as an invite-only beta.
CurrentC does have one positive thing going for it: removing the credit card middle man by connecting the mobile wallet directly to your bank account. This means it removes the credit card fees as well.
However, CurrentC also comes with some significant downsides. For example, not only does it collect all payment data (unlike Apple Pay, which keeps payments completely private through tokenization), but it also seems to collect health data and your location. It can also open you to advertising from third parties if you opt-in. If someone else is able to get access to your phone, its Terms of Service make the phone's owner liable for fraud.
Another problem with CurrentC is on the user experience side. Apple Pay is as simple as it gets; the user only has to select a card and tap the Touch ID button to pay. With CurrentC, the user has to scan the QR code of every product, and then show them to the cashier. That alone makes CurrentC completely impractical.
Seeing how successful Apple Pay already is, and how many loyal fans Apple has for its products, it seems unlikely that these merchants will win. It also helps that Apple Pay is the superior product in almost every way, from ease of use to privacy. The one exception is slightly higher transaction fees, which is probably not big enough of a downside for most Apple users anyway.