It certainly used to be the case that the only worthwhile auto-router in the industry was Cadence SPECCTRA. I think it's been renamed and absorbed into Allegro since then. Maybe others have now caught up.
I used to use it to determine how many layers, and what geometry, a board was likely to require. For example, after a few hours, it would become clear that a board really couldn't be done on, say, 6 tracking layers, and really needed 8.
Sometimes it really would come up with a decent solution to the bulk of the routing, and would require only minimal modification by hand afterwards.
Remember, it's a mistake to reject a PCB layout just because it looks 'ugly'. If it meets DRC requirements for spacing, timing, noise, differential pair routing, decoupling and so on, then by definition it's OK. An auto-router, quite rightly, does not make aesthetic or other subjective judgment about whether or not a given layout is 'attractive' as well as functional.
I'm probably as guilty as anyone of trying to make PCB layouts that look "nice" as well as work, but it's important to understand that the two aren't necessarily related.