I agree with others - tough subject but good conversation and thoughts to have.
My own personal approach is that I will try anything to treat a treatable illness as long as it is not causing my dog to suffer. I will do surgeries and chemo if they are going to prolong a good quality of life. My last dog had cancer at a very healthy 12 years old - she had surgery, she got an infection, we treated the infection, we started the chemo, but it was soon evident the chemo was not working. I actually said to my vets, please tell me if you think it is time to let her go because I'm afraid I won't see it because I don't want to lose her. They said that because I was conscious of that, they believed I would see it. And I did. One day she was okay and then suddenly she was not. She had done a very strange and peaceful act of saying goodbye to our street that evening (I can't actually explain or put it all down in words, but it was something I had never seen her do, and in hindsight, I realized that she probably knew it was the last time she would see what she was looking at), and overnight, I knew she was done. She definitely let me know. I called my vet and said, we need to come now. It was devastating and I didn't know how I was going to live without her, but I knew it was right to let her go. She was not getting better and it was not fair to her. It broke my heart and I definitely panicked that I had given up too soon, but I know it was absolutely the right time.
For Shala, she also had cancer. But she was only 8 years old. And also a very healthy, athletic 8. It was a single small tumour with no spread. She had a surgery and then chemo because it turned out it was an aggressive sarcoma. The chemo was not supposed to make her sick, but it did. She was nauseous and threw up every time. It was hard. I doubted my decision to do it, but she was only 8 years old. I felt like there was so much more potential life to be lived. I might not have made the same decision for a 12-13 year old. I'm not sure. Ultimately, I decided that a few days of feeling sick every three weeks would be worth it if the chemo worked to stave off tumour regrowth. I talked about it constantly with my oncologist and vet. She was not in pain, just felt crummy. And then the chemo was over and she was her sunny, happy self again. She had looked very sick and old during the illness and treatment, but her fur grew back shiny and full, and the grey in her face was gone. I get asked all the time now if my 9 year old is a puppy. Looking back, it was definitely a hard few months, but I am so glad that I made the decision I did. Had she been in pain, the situation would have been different. I will not let a dog suffer in pain. I think each experience informs your next one.
And I will always want to be there at the end to be holding them and telling them I love them and how they made my life better for being in it.