I always give a cutting board with their names on it.  Depending ont eh price of the home I also give a Cutco knife. 

I have never make it a practice to give closing gifts. However, many real estate professionals in our area do give gifts after the settlement.

I give the atomic clocks that tell inside and outside temperature and humidity and moon phase. I like to give something with shelf life. 

I was always a listing agent, and my builders received very nice holiday baskets for themselves and the family....the buyers were not mine....I was set up to cobroke everything and I rarely sold one myself....

Not in the past several years and we haven't seen that it makes any difference. 

My excellent service is their best gift.

For new home buyers, I rebate 1% of the purchase price to the buyers.

For resales, I give a One Year Home Warranty.

It really determines if the client is leaving town or if I repesent the Buyer I take it over on move in day!

Sometimes and usually a gift card

I usually do and I'll make it a different gift if I know enough about the clients to personalize the choice. For example once I paid for the final cleaning for a seller that was short on cash before closing. But everyone appreciates a gift card!