It is generally accepted that mountains form as the result of collision of tectonic plates, as the wording of this question assumes. However, that view is not without well-regarded critics. Cliff Ollier and Colin Pain, in their book The Origin of Mountains (Routledge, 2000), point out that the term "orogeny," which originally meant mountain building, now refers to the folding of rocks. In the minds of many, including many geologists, however, the two concepts are somewhat conflated, as it is widely assumed that the two kinds of process go hand-in-hand. Not only plate tectonics, but also the dominant contraction theory which it replaced, have assumed that the process that causes mountain uplift must also be one that causes folding of rocks. However Ollier and Pain take a contrary view, with copious reference to field studies: "Since many mountains are not on folded rocks, and for those that are, there is no relationship between the timing of folding and the timing of uplift, it seems clear that the folding did not make the mountains" (Pain and Ollier, 2008). They distinguish four types of process:
"1. processes that cause folds and other structures;
2. processes that make planation surfaces
3. processes that cause uplift of a plain to form a plateau (gentle bends, monocline, fault block (horst), tilt block);
4. erosional processes that dissect a plateau into mountains (basically fluvial and glacial)." (Ollier and Pain, 2000, p. 4)
In fact, they argue, the last three types of process represent the sequence of events common to most mountains, whereas processes of type (1) are inessential. This sequence also provides a means to provide a lower bound to the ages of present mountains: They cannot be older than the formation of the planation surface, which can be dated stratigraphically.
The mountains of western North America are the subject of chapter 5. With regard to the timing of the sequence in the Rockies, they write:
"Most workers now believe that a single, widespread erosion surface exists in the Front Range, commonly named the Rocky Mountain, Sherwood, or Late-Eocene Surface.... In central Colorado it is demonstrably late-Eocene [circa 40 Ma], but in much of the Laramide and Medicine Bow mountains it is Miocene [5-24 Ma].... Sato and Denson (1967) noted an increase in grain size of sediment, and an increase in basement-derived heavy minerals in Late Neogene sediments as evidence of uplift and erosion of the northern and middle Rocky Mountains during Late Miocene and Pliocene [1.8-5 Ma] time. Eaton (1987) presented evidence for rapid epeirogenic [a term which denotes uplift of a broad aread] uplift of the southern Rocky Mountains starting between 4 and 7 Ma."
Nevertheless, regardless of such findings, the theory of plate tectonics continues to be the governing paradigm in literature on the Rocky Mountains. Ollier and Pain list some of the problems associated with such explanations:
"1. [The Rockies] are rather far inland to be explained by plate tectonic subduction, as are all the mountains of western North America except the Coast Ranges.
2. Plate tectonic explanations of the Rockies invoke subduction at the edges, but because of the symmetry around individual blocks, it is necessary to have subduction in opposite directions.
3. The Rockies are separated from the ocean and any ocean-continent subduction site by the extensional Basin and Range Province and the Coastal Ranges, which are also explained by some as due to subduction.
4. The most general problem is that although the plates have allegedly been colliding for over 100 million years the uplift is confined to the last few million years.
5. With subduction of the Pacific Plate, one might expect tectonic features to be arranged north-south. This is fine for the Front Range and a few others, but the thrusts (or gravity slides) occur in all directions, and the problem is especially acute where the ranges run east-west, as the Uinta mountains....
In summary, the main problem with plate tectonics in North America is that so many variations on the theme have been used, including subduction, accretion of plates, strike-slip faulting along north-south lines associated with east-west compression, and various aspects of magmatism." (p.111)