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The accepted theory for the formation of our Solar System is from an accretion disk. A molecular cloud is thought to have collapsed under its own gravity and formed a disk. Most of the matter in the cloud formed the Sun, and the remaining matter was either ejected or formed the planets and other bodies (e.g. moons, asteroids, comets).

Question: Now that we've discovered many extra-solar planets, are there theories differing from the accretion disk theory for the formation of planetary stellar systems?

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    $\begingroup$ Not that I know of. After all, we can see the planets form in those disk. We measure the statistical masses, which (in the early disk stages) fit those seen later in planetary systems. Other channels, like direct cloud-collapse are difficult, because you easily end up as brown dwarf, or more massive. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Apr 26, 2021 at 17:09
  • $\begingroup$ The capture of rogue planets via drag from the disk is a way. $\endgroup$
    – WarpPrime
    Commented Apr 26, 2021 at 17:22
  • $\begingroup$ @fasterthanlight: How did those rogue planets form then? $\endgroup$
    – AtmosphericPrisonEscape
    Commented Apr 26, 2021 at 17:38
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    $\begingroup$ @AtmosphericPrisonEscape Perhaps via an accretion disk :) But it would also be possible if the planet formed like a star, but its Bok globule never had enough mass. $\endgroup$
    – WarpPrime
    Commented Apr 26, 2021 at 17:40

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The current paradigm for understanding the formation of the solar system (including the planets) is nebular theory, which is thought to be applicable to the rest of the Universe.

Question: Now that we've discovered many extra-solar planets, are there theories differing from the accretion disk theory for the formation of planetary stellar systems?

Not in terms of modern scientific theories - at least not that I am aware of, but this is outside of my expertise. I am willing to be wrong here. My point here is that if you consider the long history of proposed hypotheses of the formation of the solar system (which includes the planets) as "alternatives," then you could consider some of them in some special cases, perhaps, but this is pure speculation. Most of these historical hypotheses have been ruled out. There are issues for the contemporary nebular theory, for examples, explaining the origin of planetesimals, and explaining the discrepancy between the observed and theoretical angular momentum of the solar system.

Regarding exoplanets, I am also not aware of any system that currently definitively challenges the nebular/accretion formation paradigm (again I could be wrong here). However, mechanisms such as disk migration are used to explain the properties of many exoplanets.

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