I think putting routines are extremely important. I know because I didn't used to have one. The routine is crucial because if you stick to it, you are less likely to have the "gremlins" creep into your head. Your focus is on the routine, and pulling the trigger is just part of it. There's a considerable amount of research to support the idea that a routine improves performance.
My routine is simple, and I confess I stole if from a movie (The Greatest Game Ever). The routine is: Read it, Roll it, Hole it. Read it = I get an idea of the line, then align the line of my ball with this line. Roll it = Get in the stance and take two practice swings at the correct speed. Hole it = Get over the putt, and align the putter with the line on the ball. I don't look at the hole, all I think is speed. I take a breath, let it out, and pull the trigger. I don't lift my head till the putter has stopped. I actually do a drill now with 6 footers where I listen to see if I made the putt. That's fun drill. I made 9 in a row in my last session. Of course the practice green is always different since you have a real good idea what the putt will do and you may not on the course.
I like this routine for a couple of reasons. First it's very simple. Second, I like the self-statements. It's good to have positive thoughts over a putt. Again it keeps the gremlins at bay. Third, well I just think it sounds cool!