If its something major probably not unless you are well equipped with tools and know how. Now a water pump, or something like that, it will save you a couple of hundred dollars and doesn't take long. Now having said that if your time is more important to you than the money I would take it to someone. After you work all week who wants to spend all day working on a car. Time to relax and have some fun.
In my youth I did as much maintenance as I could, and I am both mechanically inclined and enjoyed the work. It was cheaper and that was important too. It wasn't time wasted.
When I was 33, I was laying on a piece of cardboard on the snow under my car skinning a knuckle as I loosened the oil filter. I decided it was no longer worth my time and I gave it all up, except bulbs, fuses, that sort of thing. I value my time much more highly and I prefer to pay to have other people do the work.
A friend of mine has a 1956 Porsche 356A that his grandfather bought new and we both like working on that. The car makes it pleasurable.
If I get to the point where I have sports car, or classic muscle car, or antique car (would really love a Pierce-Arrow or an old Mercury maybe) I will no doubt work on it too.
Love of the vehicle, love of doing the work, love of not paying a mechanic hundreds for a couple of hours' work - these are all excellent reasons (for me) for doing the work yourself.
If you feel confident in your ability to perform routine maintenance yourself, and are appropriately equipped, then it really depends on which you have more of, time or money. If you're really busy and time is at a premium, then it may be worth it to have a mechanic do routine work on your car, but if money is tight, then take the time to do it yourself and save the bucks.