'How hands-on is the mechanical engineering program?"

I'm going to answer this question very truthfully. The mechanical engineering program at UC Davis is not particularly hands-on. However, it doesn't mean that other schools are "better" or "worse" based on the amount of hands-on you can get. I've heard that Cal Poly San Luis Obispo has more hands-on...but I'm not one to speak on the details. This is what UC Davis does have for it's undergraduates:

• EME 50. A machine shop class where you get to be both the engineer and the machinist. You learn the basics of drill pressing, milling, and lathing.  You also get some experience with the automated processing and how to change 3D drawings into to cutting paths.
• Student Design Teams. There are 7(?) student design teams where you are part of a team to create a racecar (hybrid or off-road), RC airplane, concrete canoe, human powered vehicle, or robots (multi-function) and compete against other teams.  It is, unfortunately, on your own time, but it is very worthwhile for those students who do see a project from idea to completion. 
• Undergraduate Research. UC Davis is the biggest research UC, which means there are multiple opportunities for research. If you want tips on how to get a research gig, click here. If you need a reason why, click here.
• Senior Design/Capstone Project. I am currently working on my senior design with 4 other mechanical engineers.  You pick a project (or one gets assigned to you), and you need to meet the requirements of  your customer...don't worry, this person isn't imaginary. It requires 2 quarters of designing, analyzing, and prototyping your project. It takes you from the beginning stages of a design to the end product. You also get to use the tools you use in EME 50.  At the end, you present your work to industry representatives...and could potentially get a job out of it. Pretty cool, huh? 
• Miscellaneous Projects. Sometimes, you get really cool professors who have you work on a project. Such as for my EME 150 A and B classes. For my EME 150A class, my friend and I created a "Self Drying Towel Rack." It was pretty awesome...it even had a timer. EME 150 B consisted of the Shigley Hauler Project which you can read about here, here, and here. 

See! UC Davis is a wonderful place to study and get hands-on experience. It just may not be incorporated directly into your degree program...which I think can sometimes be a good thing. :-)

-Serena