Do I have to sign a recommendation letter that will be submitted online?
Personally, I always sign my recommendation letters, including the ones submitted electronically.  In fact, I'm not sure I've ever submitted a physical recommendation letter.

I do this for two reasons:


In the United States, at least, it is still quite strongly the custom for such letters to be signed.
It at least proves that the person writing the letter has access to a copy of my signature.


Now, both of these might be a bit archaic in our modern networked world, but the customs haven't really shifted yet, and until they do, it's good to keep doing it the way that will be expected by many recipients.

That said, you certainly don't need to go through the hassle of printing, physically signing, and scanning: if you have a high-resolution image of your signature, you can affix that as an image in the appropriate part of your document.  Some word processors or PDF editors will also allow you to "digitally sign" and associate this with some form of cryptographic signature.

In short: sign your letter, but do it the easy and electronic way if you can.