Biotic abilities are of varying rarity and status in other species:
All asari are naturally biotic to some degree, and though not all choose to develop their abilities, those who do pursue training usually display formidable ability. They do not require implants to use biotics effectively, nor do they need to undergo special training to acquire conscious neural control; their reproductive physiology grants them this ability from birth. Biotic ability is mandatory for asari who want to go into military service. The most powerful train as asari commandos.
Salarian biotics are unusual and highly prized. The salarian military does not risk them in the front lines but instead uses them in intelligence services.
Turian biotics are also uncommon, and generally not much more powerful than a human L3. They are viewed with suspicion by the general turian infantry and tend to be relegated to special units called "Cabals", which are employed for key missions.
The few krogan biotics are extremely powerful and often train to become krogan battlemasters like Skarr or Wrex. Before the genophage, biotic krogan who enlisted in the military would rise quickly through the ranks; the other soldiers were in fear and awe of them, so their superiors recognized they would command great respect as officers and promoted them. The krogan developed a surgical procedure that was able to confer biotic ability, but the operation had a high mortality rate, so it was discontinued following the release of the genophage.
According to Tali, quarian biotics are very rare. It is speculated that this is due to their life aboard the Migrant Fleet. Element zero is such a rare resource that it is probably too precious to be 'spent' on encouraging biotic potential in quarians, and because the quarians live aboard ships, any engine accident severe enough to release dust-form element zero would also be fatal to the crew.
All Collectors have a latent biotic potential which is activated if the Collector General takes control of their body and mind, transforming them into powerful and dangerous opponents.
Rachni Brood Warriors appear to have some biotic abilities.
There are known batarian biotics who are trained as shock troopers and sentinels.
The drell assassin Thane Krios is a biotic. There are multiple biotic drell who take up the fight against the Reapers. It is unknown if these drell are specialists or common drell.
Javik is a Prothean biotic. It is unknown how widespread Prothean biotics were before their extinction.
To date, there has been no mention of the biotic abilities of the hanar, elcor, raloi, volus, vorcha, or yahg or what role (if any) biotics play in their respective societies.