There are many examples.
Vulcans: The Vulcans have large racial diversity. TOS's Spock, VOY's Tuvok, and ENT's T'Pol all appear to be different ethnicity. Furthermore, the Romulans are still biologically similar enough to the main Vulcans to be inter-compatible, but they're distinct enough that certain medical treatments won't work the same, as mentioned in DS9's Inter Arma i'm not typing the rest of that name. If standard medicine has to be double checked for different ethnicities, you have an extremely diverse species. Also, most Romulans are white or slightly tan colored. However, in DS9's "Improbable Cause", we saw a black Romulan woman who worked for the Tal Shiar.
Andorians: The Andorians have a fair amount of diversity, but it seems to be skewed. The most frequent ethnic group we saw was the blue-skinned Andorians, such as Shran. We also saw in TNG's "The Offspring" that green Andorians exist. We saw the Aenar in Enterprise, who are blind, telepathic, and white. This species likely will have a genetic bottleneck, as their population is dropping, and the Aenar are extinct. http://en.memory-alpha.wikia.com/wiki/Aenar
Trill: as mentioned by @Mr Lister, though most trill are the spotted kind, there's also a forehead ridged kind.
Bajorans: as mentioned in the memory alpha page, there were dark skinned Bajorans. This was never a plot point. http://en.memory-alpha.wikia.com/wiki/Bajoran
Ocampans: We know that some of the Ocampa left after their world was transformed into a desert. The two groups lost contact shortly thereafter, and were seperated for at least 300 years. At a rate of complete population replacement every 9 years, the two groups have been seperated for well over 30 generations, which would be enough for some genetic distinctness to emerge, especially since the seperatist group was only a few hundred people. The small population would likely have a fair amount of genetic shift, enough for some distinctions to emerge. http://en.memory-alpha.wikia.com/wiki/Ocampa
Jem'Hadar: We know that after Sisko mined the aperture of the Bajoran wormhole, the dominion had to start cloning Jem'Hadar locally in the alpha quadrant. These Jem'Hadar were apparently breed with different demands in mind. This may be the only example of deliberate artificial racial diversity. http://en.memory-alpha.wikia.com/wiki/Jem_Hadar
Kobali: Probably the most extreme example in terms of variety. This species grows its population by salvaging the dead of other species, modifying the dead to meet their biological specs, and being a race of zombies. The process isn't perfect, and as a result, people retain enough origional DNA to be individually identifiable. As a result, the Kobali have the racial diversity of the variation between several different species. http://en.memory-alpha.wikia.com/wiki/Kobali