Having done a degree in biology about ten years ago, I'd have said not. That was before my mum (who is a university botanist) brought this plant home called the "sensitive plant". I think we were having a disagreement about whether or not plants can feel anything and she wanted to prove it's possible for them to feel touch.
The sensitive plant can feel when you touch it, and it moves. So although it doesn't have nerves or muscles like animal tissues, it definitely has something to feel with, and it can feel the slightest touch. It can also react instantly to it. I got told.
A ticklish plant!!! XD
That's freaking awesome. I want one!