If you aren't already aware, let me tell you there's been tons and tons of art created for The Lord of the Rings. Of course there were the Brothers Hildebrandt's calendars I posted about recently, but there's so much more.
I'll start with the covers for the editions I grew up with. The first are wild, psychedelic paintings by Barbara Remington. She hadn't read the books when she created them but had to go on a synopsis from a friend. So the original cover for The Hobbit she did had a lion and fruit that looked like some sort of wild gourds. Later versions removed the cat, but left in the pumpkins.
The second covers I became familiar with were paintings by Prof. Tolkien himself. I love his paintings, all washed out colors and faceted like something hand carved. I'll do a full post of his artwork soon.
The Remington covers were so popular they were made available as a poster. Her work was lampooned on the cover of Bored of the Rings as well.