I notice that when I move my fingers off of a string to go to another one, more often than I'd like the string will ring out and ruin whatever it is I'm playing. Its as if I'm slightly "pulling off" but I'm not trying to. I can only stop it if I really slowly let off the string which of course is hard to concentrate on when you're playing riffs. This is especially noticeable with high gain, I'll be playing like the sweet child of mine intro and the next thing I hear is a horrible open string twaaang to ruin it.
Take it off softly would be the best advice, without pulling down to create a pulloff, although I'm sure some of the other guys have better ideas though.
Everyone has their own fix to this one...some people kinda do a light(VERY light) palm mute sort of thing, which stops that string from vibrating without touching the other strings that are in use. some use their left hand. some just dont have this problem you just have to find a technique that works for you. sorry if that doesnt help much
pulling off softer just takes practice and experience, combine it with a combination of left and right hand muting of the string you're pulling off. like unless you're fretting with your pointer you can use your pointer to kind of catch the strings before they sound out. also practice your finger walking. if you are pulling off with your pointer, maybe wait until you're fretting the next note with another finger and slowly pull off.