"Is there a rule of thumb for yearly pay raises or cost of living pay raises when you do not get a promotion?"
Got my mind on my money...
Generally companies will offer a cost of living pay raise annual to cover the annual increase of inflation. COLAs, or Cost of Living Adjustments are not required, and it is up to each company's discretion whether or not they offer them.
In August of last year, Tower's Watson published a study of over 1,100 large employers that found a 3% increase on base pay was the average COLA planned for 2016 by large companies in the United States. They also found that individuals with high performance ratings could expect an average salary increase of 4.6% (that is, if you have performance reviews). There are some interesting statistics on planned average bonuses for 2016 if you really want to get into the numbers here. And, if you really want to geek out, Kiplinger has a very interesting breakdown of how and by how much the cost of living will increase in America in 2016.
Again, while companies are not required to give COLAs, it is widely accepted practice. In the study from Tower Watson they found that only 1.9% of the companies surveyed did not plan on granting pay raises, so the chances that you got some money coming your way are pretty good.