Stories where the villain is in love with the heroine?

You should not have problems finding that, it is a very common element.

But a difficult one to remember!

I started thinking and could not recall a single one then I had my Doh moment.

Ivanhoe fits perfectly, and it has some very interesting twists on the theme.

Doh, 'Last of the Mohicians' uses the same element, in a way twice, or perhaps one and a half times. Or is it half twice? It being a more complex book one could cast at least 3 characters as villians, one of those is clearly in love with the heroine. But it might be more accurate to call the individaul involved a minion, so not the lead villian. (And it may not fit the emotional idea you are looking for, he is a good man in many ways, very much not one who seeks to win hte heroine using the methods of a villian).

Bram Stoker's Dracula, totally addicted to Mina's blood!

Many classic gothic romances play with this trope: anything (I think) from Ann Radcliffe, The Mysteries of Udolpho is a classic.

Heathcliff in Emily Brontë's classic Wuthering Heights, truly madly in love with Catherine; a little less "madly" Rochester with Jane in Jane Eyre.

Northanger Abbey by Jane Austen: Catherine Morland is pursued by the dubious John Thorpe; ditto Wickham-Elizabeth in Austen's Pride & Prejudice and William Elliot-Anne in Austen's Persuasion.

Henry James's The Portrait of a Lady and Jack London's The Sea-Wolf both feature a truly sociopathic villain in love (well, in lust at least) with the heroine.

E.M. Foster's A Room with a View, although Cecil Vyse is pathetic rather than passionate in his love for Lucy.

In the Russian classic Doctor Zhivago by Boris Pasternak, two villains pursue the heroine, Lara: her mother's powerful lover Komarovsky and Pavel, her childhood friend-turned-Bolshevik hard-liner.

If you like westerns, the many Zane Grey novels have the villain/antagonist's pursuing/intending to marry/kidnapping the heroine: Riders of the Purple Sage (Jane's & Bess's evil LDS Elder Tull), The Border Legion (bad border bandit Jack Kells kidnaps Joan), To the Last Man, The Mysterious Rider (Columbine's step-brother "wild" Jack), The Light of the Western Stars.

Sookie Stackhouse The Southern Vampire series by Charlaine Harris (if you are not familier with the novels/HBO series yet!).

If (low) fantasy is to your taste:
The Wolf Of Winter by Paula Volsky,
which would recommend anyway, because Varis is imo one of fantasy's best villains/antiheroes ever.
Actually the topic is present in some form in several of Volsky's novels. For example in The Grand Eclipse, in a way.

It also appears frequently in Tanja Kinkel's historical/fantastic books (like Mondlaub or Unter dem Zwillingsstern), it doesn't look like they have been translated into English, though.

Also, of course, Victor Hugo's The Hunchback of Notre Dame.

Outside of literature (since you already mentioned Disney's version of Beauty and the Beast) there is also Buffy The Vampire Slayer (season 4 onwards), even if Spike gets turned to good towards the end.

The Black Moth by Georgette Heyer. Very good story...

Mmm, that'd be this Amazon.com: The Stone of the Stars (The Dragon Throne, Book 1) (9780446690980): Alison Baird: Books