For example: "This car is the ultimate best."
Yes, it is.
It is widely used in books, too:
Use "very best" instead if you want to emphasize "best." "Ultimate" means "final" and "best" defines the most capable or favored. If something is the most capable or favored out of all other things, then it is also the "ultimate" thing, because why would you need other things when you already have the best one?
"Very best" has an application because "best" can also be used to define an elite group, not the singular most capable:
The Honda Accord is one of the best cars ever made.
Here, "best" clearly defines an elite group, not a singular "best car." Using "very best" sets a singular thing apart from even the "best" cars.
"Ultimate best" may make sense from a purely logical, technical perspective when you take into consideration that new things which come out are often better than old things, but it's very awkward and unidiomatic because "ultimate" usually implies that it is already best of its class. If you wanted to say that a model of car was so good that it will be better than any car that comes after it, labelling it "the ultimate car" gets that point across just fine without stating "best."