I've been in business for about 10 years and never sent one out.
I think your customer will appreciate your honesty much better than any thank you cards.
For example if you see anything wrong around the property, say a clogged gutter, a snake hole... call him/her up and let them know, they will be your customers for life.
Also if you ever happen to break anything, say smash a gutter down spout, mow over a hose... Be the first one to contact. More cases than not, the home owner will be so appreciative that they might not even want to charge you for your mistake.
Bottom line is, it can be done, but showing your honesty and broad vision will keep your clients for life much more effectively.
Hope it helps