Do university rankings matter for research?
I think the importance you have to attach to this criterion (university ranking) when finding a new research job (from your question, it appears to be a PhD) is limited, because:


What counts if our research output: your results, and how you communicate them to your community. You want people in your field to recognize you as someone who can tackle difficult problems and design creative and efficient solutions.
Of course, your research may not be so stellar that everyone has heard of you. So, coming from a well-known group with a proven track record is important. You want your research group to be famous, because it reflect well on you.
But it's not that simple… not all group leaders are superstars! Failing that, it is better to be affiliated with a well-known department (or university). You want to be in a university/department that people think is good.
But not all people know all universities well enough to be able to judge them. Those who don't rely on externally published rankings.


See how rankings are introduced only as item #4 in the above list. Thus, even considering only the career advancement side of your question, university ranking is not a primary concern. Sure, it plays a role, but lots of students overestimate that role compared to, say, the importance of your own work and results.