If people just learned the basics of maintaining and repairing vehicles they'd save themselves thousands of dollars by buying auctioned off used cars and repairing it. Same thing for taking it for a shop for maintenance...
I think knowing how to fix cars is valuable, but I don't think doing maintenance yourself generally pays off. I'm pretty handy with a car, but the only maintenance I do myself are brakes and batteries. Tires require special tools, so those are out for the shade-tree, same with suspension (which requires alignments after installation). I've found that oil changes, air filters, wiper blades can be done at the dealer for about the cost of parts (at least for my Ford and Toyota).
Now, as far as fixing repairs. Most mechanics, especially at dealerships, will toss parts at the problem. So knowing how to research the problem can help save you a boat load of money, even if you do none of the physical work yourself, since you can come in and ask for them to perform some specific fix. Additionally, lots of sensors are easy fixes if you can follow direction on YouTube/forums.
Kinda depends on how much an hour of your time is worth. Maybe an oil change is worth paying someone for (most shops don't charge much for an oil change). If you are really mechanically savvy you can save hundreds of dollars though.
I bought an extremely-cheap Evo X (like ~$5k cheaper than average)....the car came with a bad Active Center Differential Pump, which is a $1500 part. I ordered the part at Mitsubishi then put my car on jack-stands at my home and changed the part myself. Then ran the computer software necessary via my laptop and a specialized cable to flush the pump fluid as well. Took me a Sunday afternoon but saved me hundreds of dollars in labor. Plus I now have a car with a brand-new pump that still cost me THOUSANDS of dollars less than any other Evo X that was on the market here.
Edit: Of course, you'll want to drive it to an alignment shop right away.