I didn't. I'm reading salems lot now and I read the whole DT series a little while ago. If you have read a connecting book, when the character/s appear you will know their background and story already. If you read the dark towers 1st, then you read (for example) salems lot, when you come across the character from the DT you will have some knowledge of them from that.
If you're going to read all of his connecting books first then you won't be reading the dark towers anytime soon, there are a LOT of them.
To touch on NN's point about the gunslinger, I know I'm repeating myself but imagine the dark towers are one very big book, then the gunslinger is the first 30 or so pages of a normal book. It's the intro, it's setting the scenery, giving you a little taste. She's right though, it starts properly with drawing of the 3