So, did some Sith wield a non-red (non-synthetic) lightsaber?
And the other way around, were there some Jedi wielding red ones?
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In EU: Exar Kun, Darth Vader and Darth Sidious
In Canon: Anakin Skywalker
Wookieepedia explains that:
However, the bloodshine blades were not universal to all Sith, with notables such as Exar Kun and Darth Vader continuing to favor their blue Jedi lightsabers after defecting. However, Kun was likely unaware of the custom, and Vader replaced his Jedi weapon with a red-bladed Sith saber soon afterwards. Darth Sidious also used a pale blue colored lightsaber after his reincarnation. Ultimately, Sith who wielded colors other than red were usually looking to disguise their dark affiliations. In fact, Palpatine was of the opinion that the Sith Lords had outgrown the use of lightsabers, and only continued to use them to humiliate the Jedi.
So, yes, non-synthetic lightsabers have been used by Sith Lords, but not for extended periods, or not intentionally done so to disregard the custom.
We know that there were probably more than just three, as Kun's
followers opted instead to continue using their Jedi lightsabers in combat, though at least one follower used a lightsaber with a red crystal
More specifically, in canon, we have only seen one: Anakin Skywalker
More generally though, as to why most Sith use a red lightsaber is explained in the same article as follows:
the defining feature of Sith lightsabers was the use of synthetic crystals, as opposed to the Adegan and Ilum crystals favored by the Jedi. Almost all synthetic crystals used by the Sith featured a red coloration
The article goes on to explain that:
Originally, Sith Lords utilized synthetic crystals due to their lack of access to the traditional sites where crystals were harvested, as these were frequented by the Jedi Order. Eventually, the use of these synth-crystals became a tradition amongst the Sith, who believed the creation of a crystal suited to one's own needs was a display of strength over the Jedi, who relied on the "untamed wilds of space" to provide.
The red coloration was also a result of the forging process, though it too came to become a tradition. The aggressive crimson hue served to differentiate the Sith from their sworn enemies; the Jedi, who typically utilized softer colors, commonly blue or green
In addition of Often Right's answer, in Legends video games, we can see Sith and Dark Jedi wearing:
If you want to limit to Sith only and not Dark Jedi, you still got red and purple lightsabers.
Red is the most frequent color because it is made with a synthetic crystal which is easier to obtain, and you know most dark side users always go for the path of least resistance.
However, there are Sith using other colors, and dark jedi as well.
Anyway, I wrote an in-depth post on sith lightsabers that I think may be useful, but this pretty much sums it up.
EDIT: Summarizing the info on the source link in case it goes bad:
In addition to the other answers
Vergere used a Yellow lightsaber
Lumiya used a yellow light whip (if you want to count that since it isn't technically a lightsaber)
Grievous had two Blue and two Green lightsabers (although he wasn't technically a Sith or even a force user)