For me, doing my own repairs has paid off huge! I have recently replaced a badly scratched camera lens cover on my phone for $5 (instead of $50), purchased my own windshield wiper instead of having someone else replace it ($10 instead of who knows how much), installed new belt/tensioner/support wheels on my dryer ($15 instead of $75+), and replaced a water pump on my washing machine ($10 instead of $75+). I also cook almost all my own food (immeasurably large savings), including fancy dinners ($20 for ingredients instead of $60+ at a nice place). I glued a chair together that had fallen apart ($5 worth of glue I can use many times, instead of $100+ for a new set of chairs) and have done a LOT of basic plumbing and electric, mostly fixing switches, cleaning and maintaining electronics instead of buying new, and installing my own shower heads in my apartment (really this one cost me money, but having the shower head 7 feet up is pretty dang nice!).
For me the biggest thing benefit is the pride walking around my home and knowing that I can take care of the things I use. Being self-reliant on lots of the basics gives me a lot of confidence that I'll be all right if something stops working, and lets me customize things to exactly how I want them. Now that I've mastered a few of the basics I know I can always learn more, and when I move out of this apartment and in to a house I know I can do minor renovations, upgrades, and earthmoving on my own. The money comes in to play when I see friends spending for that stuff, or being worried they may need some basic repairs done and keeping money put aside for that stuff, while I can put mine to work making more money instead!