There are applications of biomimicry in nearly every aspect of space exploration, ranging from the algorithms used to guide spacecraft to the locomotion of rovers to even the structure of spacecraft and the rockets used to get them to space.
The long answer
First of all - thanks for asking this question! It's one that doesn't get asked nearly enough - biology often gets a bad rap from folks in the space sector, as some of its more 'obvious' applications (human spaceflight, astrobiology/planetary protection, terraforming) don't appear to have direct applications to the process of actually building spacecraft and instruments that can travel to and operate in an environment where - as far as we know now - life doesn't exist (at least not in a form that we currently recognize). As a result, you don't necessarily see as much in the way of biologically-inspired elements in aerospace (or research into such elements) as you see in other sectors - but that doesn't mean that such elements aren't still an integral part of space exploration.
Machine learning, for instance - the new 'hot' topic in computer science that has found uses in spacecraft operations support, guidance and control, etc. - has its roots in evolutionary processes to a fair extent, and is loosely based on how the brain works (hence why the term 'neural nets' gets bandied about these days). Incremental evolution has even been used to select design parameters for NASA spacecraft. Similarly, the algorithms which might be used to guide future swarms of spacecraft are biologically inspired by the behavior of flocking and swarming organisms (birds, insects, etc.) here on Earth.
If it's physical spacecraft components you're interested in, not just the algorithms used to design and operate them, you'll still find numerous examples of biologically-inspired design. Astronaut seats on spacecraft are being redesigned to better handle impact forces based on the kinematics that allow cats to land nimbly on the ground; armadillo carapaces are being studied by the US Air Force as a design reference for the cylindrical shells on rockets; thermal control systems on spacecraft and satellite panels are being designed to mimic the human circulatory system; rovers have been proposed which use locomotion methods inspired by tumbleweed; the European Space Agency (ESA) is even looking into designing a cockroach-inspired landing device for its spacecraft. There are quite a few other examples; NASA's Glenn Research Center maintains a list of a few projects which NASA is actively working on. There's also been discussion of other potential aspects of space exploration that biomimicry can contribute to; see, for instance, this article here.
These are just a few examples of how biology has influenced design in space exploration, and that's not including biologically-inspired inventions like Velcro, etc., which aren't necessarily aerospace-specific but which (like you mentioned) were designed for/used by space exploration missions.
In short - millennia of evolution have effectively made nature the universe's best engineer (though I'm sure there are a few who would quibble with me on that!), and it's always worth keeping an open mind to what biology has to offer.