I started out as a "lab monkey" during the summer after my sophomore year in an organic chemistry lab. It was essentially interactive shadowing for about 2 months (not to mention my assigned postdoc was a d*ck.) I continued to work through the fall semester and by the end of the semester (about 6-7 months after starting) I was mostly independent. During the spring semester, I was given a project towards a total synthesis of a natural product that was completely my own. Since then, I've started a new project where I have the authority to freely order compounds (that cost less than 100$/gram) and glassware, work whenever the hell I feel like it (as long as I can present results to the PI bimonthly) and have also started to train new undergrads. I'm sure a lot of research experiences are cookie cutter type bull **** but definitely not all of them. I've loved (and absolutely hated at times!) my experiences and feel that research, similarly to a crappy 9-5 job, is what you make of it. You can lull through it and end up a lab monkey or you can bust your ass and move towards better things.
tldr: research is what you make of it