How should a mathematics major choose between doing a Masters or PhD? I would really appreciate any advice or suggestions anyone might have. I am currently a senior mathematics major, about to graduate in May. For two years, I have planned on going for my PhD in pure mathematics (my highest interests have been in algebra, number theory, and discrete math). I applied to 8 PhD programs and 1 masters program, the masters program just for the heck of it. I was accepted into the masters program, but I was rejected from 6 PhD programs and wait-listed on the other two. Neither of these last two would I really want to go to, but I would be happy at either of them nonetheless. 

Now, the masters program is at Ohio State and gives full tuition waiver plus a minimum monthly stipend of $1950, plus a significantly reduced health insurance bill. The program specifically is the Master of Mathematical Sciences with concentration in Computational Sciences. The department is super lenient as to which courses I can take outside of their main core courses, as long as my course plan fits the computational theme and as long as my advisor signs off. 

So, my question is, should I go to the masters program or should I go to one of the PhD programs (if I'm even accepted; again, I'm still wait-listed)? Will finishing this MMS program at Ohio State help my chances of getting in to a top-notch PhD program in the future? How common is it (in mathematics) for mathematicians to earn a (non-"incidental") masters degree before pursuing their PhD? 

Thanks! Let me know if you want any clarification or further information.
I'm not in mathematics so take my answer for what it is. 
The fact that you were turned down by 6 PhD programs suggests that your applications probably weren't too strong. Maybe you had bad grades, bad test scores, bad recommendations, etc. Or you simply overestimated your application strength and applied to schools beyond your reach (i.e. top 15 schools). 

Whatever it is, you need to overcome these shortcomings in your credentials. A Masters degree could be a great way to prove that you are grad school material, especially if you can demonstrate that you fit in academia by publishing article(s). This could be a jumping point to a decent PhD program. Generally, graduate programs would rather accept successful masters students over successful bachelors students, simply because good masters students already know the system and how to make it work.