Sadly, I believe hand written thank you notes for small occasions has become pretty much a thing of the past as electronic communications have taken over the universe. As email and texting are now most people's preferred means of communication, I think this is acceptable for most occasions. I would not ever send thank yous for Graduations, Weddings, etc via any electronic means. I believe these should still be handwritten, as should any that are going to grandparents and such out of respect.
However, as the thank you is sent at all says a lot about about the sender, that they are a gracious person and truly appreciated your thoughtfulness.
Myrabeth - I understand your problem completely. I still remember my third grade teacher telling me I was holding my pencil in the wrong hand and making me use my right hand- THIRD GRADE!!) I write everything in block print, all caps, just enlarging the first letters where capitalization is needed. My signature is good, but I practiced it hundreds of times to get it to the point where I liked it.