Bea Yep! The stories all are stand alone. Some are set in familiar worlds, which is nice if you have read previous work from the author, but that's as far as it goes!
Rob Trans I think you can, but in the case of the Kingskiller Chronicle, you will lose some of the context if you haven't read at least the first book. Since I haven't read many of the other series I don't know if that is true for them as well.
Marthie Elice I can only speak on behalf of The Lightning Tree, if you haven't read Patrick's other books in the same universe, you should definitely read those first. They are fantastic! And then come back and read The Lightning Tree after TNoTW and TWMF :)