Undergraduate and masters research projects: You can propose your own project. In that case, come to meet me with a clear plan. If you look ambitious and wish to do the project not just to pass the requirement, I will accept it unless I am overwhelmed by a large number of undergraduate/masters projects. Usually, even undergraduate students in our group aim to publish their findings. This is good for your own careers and a reward for my effort. So, please have this above average goal in mind before choosing a project.
PhD students: Please look at the information here.