Few things are as memorable as receiving a personal, handwritten note. Especially today. When was the last time you received a hand written note? You remember the people who send them to you. And it is a great way of showing someone how grateful you are or just to keep in touch.
As far as business goes, if you want to be remembered then write a note. People tend to hang on to hand written things, so it is likely your note will hang around for a while.
I personally try and write and mail five cards a week. It is an exercise that has paid big dividends in my relationships over the years.