Is 3D printing a good way to save money? If you already have a 3D printer, would you say that you have saved money on buying the printer, buying models and then printing the models, compared to buying something alike in retail?

Would you say that saving money is an argument to buy a 3D printer?
I would say that the general answer to your specific question is no. If you want to justify buying a printer because of all the things you could print instead of buying that is not going to be easy. 

If however you are a DIYer and you have some CAD skills, or are willing to learn some, then consider the 3D printer as another tool you can use. There are plenty of stories about people who fixed some very expensive thing instead of having to buy a whole new one for hundreds of $/£; so if you have a specific use in mind then it may be justifiable to you.

I have made and fixed stuff around the house, but it's often things you simply couldn't buy, or could have fixed some other way.

There is an ever growing library of models available out there, and many are free. I recently fixed the leg on my keyboard with a printed one which I found on thingiverse, took minutes to print and the keyboard is part of a wireless set which would cost £30 to replace, so that was great but you won't normally find exactly what you want like that at this time.

And lastly it's not plug 'n Play yet, so you need to be a tinkerer at heart to use most printers out there right now.