Ugh, yes, Dany/Drogo. As far as I'm concerned TV!Drogo rapes Dany on their wedding night, which is truly unfortunate because it drastically changes the likability of their relationship. I guess they didn't have time to develop it in the beginning so they were like, "he'll just rape her, we'll fix it later," or whatever, but it comes off as lazy writing to me. Kitsune17 is probably also right; they wanted to make the Dothraki seem so very ferocious, which is also lazy writing to me.

I'd probably have a very different feel for their relationship if I'd only seen the TV show.

Read the books! Not just for a more respectful, less rapey Dany/Drogo, but because they're awesome. The prologue sometimes turns off new readers, so don't be afraid to skip it; the first chapter is amazing and will have you hooked, and then you can go back and read the prologue later.