Do commercial jets ever make 360 in the pattern for separation?
Yes, it can happen, but it's pretty uncommon.

Airliners arrive at the destination airport having been sequenced by ARTCC ("Center") and Approach so that they are showing up in an orderly sequence, spaced out so that there is adequate room between them.  They may be set up for an ILS, or they may see the field and accept a visual approach, but either way the flow is generally quite predictable and orderly.  VFR traffic, by its nature, is less controlled and ordered, so it's more likely in that sort of an operation that you'd have two aircraft in positions to arrive at the runway at about the same time, so a solution like a 360 on downwind or on final becomes necessary.  With a flow of airliners (and other IFR traffic) spaced out at 3-5 miles apart, that solution would create as much trouble as it would solve, because now the conflict is with the aircraft behind the one that circled, rather than with the one in front of it.

What does happen more frequently, is the 360 happens much farther out from the airport, and that's called "going into holding" due to traffic saturation.  Maybe the airport is over-loaded with arrivals, or it had to suspend operations while the active runway was changed from 18 to 36 (or whatever they are at a particular field), or there is weather affecting the approaches which slows down the rate at which it can accept arrivals.  The Approach and Center controllers will work to keep the flow of traffic coming into the airport neat &amp; orderly, which means delaying aircraft before they get to Tower's airspace (i.e. the "traffic pattern").  Ideally, they will do this with speed adjustments to get the desired interval, but sometimes the delay needed is more than speed adjustments alone can accomplish.  Then they'll put the arrivals into holding for however long it takes until they can start sending them in again.

That's the more common airline version of a "360 on final"... doing 360's with 10 mile legs on a really, really extended final -- 100+ miles out!

In the case of a go-around that turns downwind, rather than a 360 on final, the typical solution would be to extend turning final out until there is adequate space.  Staying on downwind past a 5 or 10 mile base &amp; final is highly undesirable for a VFR pattern, but for airliners where everybody has an ILS and doesn't really have to maintain sight of the runway, it's no big deal.  For big airports, extending the traffic pattern out to longer finals is highly preferred over having jets circling on final.