The marketing word is delighting. They are supposed to surprise you and make you feel special, however with hotel elite status the benefits are so uniform it's hard to make it individual.

Good examples:

PH MEL GM used to write me personal, handwritten notes, would always make time to meet me for a drink during my stays and we formed a relationship. He would always go above and beyond, even contacting other Hyatt hotels to ask them to look after me.

Bad example:

When he left the PH MEL the new GM printed the cards, reduced the multiple amenities of wine, chocolates and nuts that were provided to all Diamonds (you never had to choose between this or the points) the decline in service from the top with the former GM couldn't be more stark.

Other good examples:

QF sending bottles of Champagne or wine for Christmas or 'delighting' with tickets to Fashion week. Mercedes Benz inviting customers to Driving Academy Days for free (cost ≥$500.

But make no mistake, the entire purpose is build stronger loyalty from you.

And to address the op handwritten cards are proven method of delighting. In a digital world the time it took someone to hand write a note is intended to make it person. Although with some individual's attitudes mean they never get the point...