Which apps besides PayPal allow instant transfers to friends and family?

Let me answer from two perspectives:

Cross-Border Payments: There isn’t any worldwide consensus on this. Real-time payments, especially for cross-border are still not a reality for many, many countries. Each remittance corridor (pair of countries, from where the transaction is originated and where it is terminated) varies from corridor to corridor. For example in Australia to the Philippines, there may be a specific money transfer provider or an app that might be the preferred choice for sending money back home at the earliest. So, no clear definitive answer here.

Domestic Payments: Depending on the country, this varies. In India, for example, it is Paytm, in Bangladesh, it is bKash, in the UK it is FasterPayments, in Kenya, it is mPesa, in Pakistan, it is Jazz Cash or EasyPaisa, in Russia it is QIWI, etc. Every country now really has their own home-grown solution (or two) that they prefer to use for real-time payments.