What is the current relevance of Arianism? Is there an active sect by this name? Are there any particular Christian denominations which might be described as 'Arian'?
To answer this, one must first define what Arianism is. Any denomination which holds that Jesus Christ is a subordinate entity to God. He is not one with the Father. Christ is not truly divine but a created being can be considered as 'Arian'. In Arius's words, "there was [a time] when he (the Son) was not."

Holy Arian Catholic and Apostolic Church in claims to proclaim Arius's teachings, even "canonizing" him in 2006. However, they differ with several major points. AFAIK this is the only known church to explicitly call themselves as Arian.

The Jehovah's Witnesses is often accused of being Arian. JWs even regard Arius as a forerunner of Charles Taze Russell, the founder of their movement. But they do not call themselves Arian.src The main difference is that they claim that the "Archangel Michael transformed into human Jesus, then after dying transformed back to Archangel Michael again" teaching. That is not in with the historic Arian doctrine.

Some sects like Unitarianism, Mormonism (Latter Day Saint movement), Iglesia ni Cristo etc., hold a form of Arianism, but they all differ with each other and with traditional Arianism in many doctrinal issues.

No remnant of any of the Arian sects established in early days is known to exist today.