Luthien Tinuviel is probably the most fleshed-out female character in The Silmarillion - and her character consists almost entirely of rescuing herself, or rescuing Beren. When Beren is captured by Sauron, Luthien makes her own escape ('self-rescuing princess', oh yes indeed - and a fantastic inversion of the Rapunzel story), is captured by two Sons of Feanor and their gigantic hound, then escapes again, subverting that same hound, in order to lure out Sauron, capture him, and tear down his fortress. She heals Beren, works with Huan to come up with an actual plan to get into Angband, does all the work in stealing the Silmaril, heals Beren again... it is a constant tragedy that people often call Luthien a Mary-Sue. Really? Why? Because she keeps winning? Given that she actually dies at the end of it all, I think she put in the effort to deserve it.
All right, I'll expand on that. Luthien gets captured twice by the Sons of Feanor. The first time she's actually caught by Huan, and very quickly realises she's in the company of (theoretical) friends. The second time, they grab her by surprise; what I'm saying is that she's not exactly being 'constantly kidnapped'. Do people get quite obsessive over her? Yes - but not 'just because'. Thingol, of course, is her father, and wants to protect her (though his methods are seriously messed up). Beren falls in love with her. Celegorm and Curufin do not love her - they want to marry her in order to a) annoy Thingol, and b) give themselves an excuse to claim kinship with Thingol, and thus make demands of him. Huan, the faithful hound, joins her in order to save Beren (and Finrod, even though they fail!), but only permanently joins her side when he sees Curufin try to kidnap (and possible kill) her.
See a theme yet? At no point have I mentioned her beauty. Despite her being the fairest person ever to walk the planet, the only people who focus on that are the villains - although, come to think of it, Sauron didn't even know who she was (he went out to fight Huan, not Luthien), and Morgoth didn't exactly go looking for her.
Yes, Luthien is beautiful - but that doesn't define her, nor does it particularly influence her actions. Yes, Luthien is powerful - but in very specific ways. She has skill in healing, which sounds like something she would have learnt (Doriath is a realm under siege, after all). She can dance and sing - again, she's had hundreds or thousands of years to learn. And she, usually through her nightcloak, can put people to sleep. That's the one power she uses repeatedly. Luthien's skill lies in that she can find a way to make her limited powers work for her. She doesn't try to defeat Carcharoth with strength - she comes at him sideways and sends him to sleep. She doesn't try a frontal assault on Morgoth, either - she manipulates her environment to allow her to use her powers, yet again.
And yet, she does the unprecedented. She takes a Silmaril from Morgoth - and afterwards, when Beren has been killed, she goes into Mandos and brings him back. We're told that she sang or danced before the Doomsman and moved him to tears - but we're not told how. Nevertheless, knowing what we do of her, we can make a guess: her power lay in sleep, and in dreams. To the Eldar, memory is more like a waking dream than a misty recollection. What else would she have done, but woven her tragic tale into a song - and driven it straight into Namo's heart?
Yes, Luthien is powerful. Yes, Luthien is beautiful. Yes, Luthien is capable of finding a way to turn any situation to her advantage. But is she a Mary-Sue? No. Around her, people continue to act according to their own desires, their own goals, their own plans. She just - by virtue of her birth, mostly - happens to be central to many of those schemes. Nothing more.