I actually slid into reading romance novels by reading a mystery series that had a complex, believable romance intertwined with it. Even though the two main characters get married in the second or third book, the author takes her time exploring this relationship between a Hispanic divorced, former narcotics cop (reformed alcoholic), and a young widow in California over the course of 7 or 8 books. The clash of cultures, backgrounds, and experiences that were frankly more interesting than the actual mysteries. Her books didn't have any sex, just sexual tension, romance, and relationship struggles. (The author is Earlene Fowler and her books are found in the mystery section of the bookstore, not romance).
I was reading Fowler's website when I clicked some links to "romance" authors. Fowler admits her books cross genres, and obviously enjoys both romance and mystery books. I've since come to understand that romance crosses boundaries with mystery and sci-fi/fantasy so deeply that some books are shelved both places in bookstores. BTW- romances are loosely divided into historical, contemporary, paranormal (werewolves, vampires, etc), sci-fi, and suspense/action.
Okay, so that sets up the background. From Fowler's link I found other authors and started checking them out at the library. I started with mysteries. Charlaine Harris has several series, and they vary in their sexual content. The lighter series is the Aurora Teagarden series. A grittier series, with more sex, is the Lily Bard series. Her sexier, much weirder, often humorous series is the Southern Vampire (also called Sookie Stackhouse) series. The HBO show True Blood is based on these books.
From the mysteries with some sexual content, I "graduated" to the romance with a little action/mystery. ;-) The difference is subtle sometimes, but the major component is that the relationship is as important as any other plot line in the book, maybe more so. One of the first authors was Susanne Brockman. She writes a decent suspense/action book filled with hunky ex-Navy SEALS and such. Her plots and characterizations are decent. Her story is as important as the relationship, and she's good with the sexual tension part. Many of her books are about the same group of people, just focusing on different characters. One main character is gay. She has a gay son (she writes about him in a moving prologue), and she does a decent job with that character and his relationship. Two of my favorites are Bodyguard and Flashpoint.
Other decent suspense/romance or mystery/romance authors where the plot is as important as the romance aspect.:
Susanne Enoch (series starting with Flirting With Danger)
Nora Roberts (She writes all types of romance, and she writes futuristic detective type stories as J. D. Robb. One of my favorites is High Noon- not a western, btw.)
Linda Howard- some are good, some so-so.
I enjoy sci-fi and fantasy, and some of the better books of the romance genre are cross-overs in these categories. My favorite author is Linnea Sinclair. She writes strong female characters who aren't dominated by their sexy male counterpoints. She writes good sci-fi plots and has well-visualized universe. Games of Command is probably my favorite, but I've liked all her books.
Other good sci-fi/fantasy authors:
Patricia Brigg (especially her Mercy Thompson series. She is not a romance author, but romance is part of her books. She is probably considered a YA author by some, but one or two of her books get a little racy for young teens.)
Okay, please note: Many of the books I mentioned have fairly graphic sex scenes somewhere in the book. Mostly the characters aren't married when this happens. If you don't like reading about pre-marital sex, these books aren't for you. ;-) If you'd rather no sex, one excellent author of Regency period romances, known for historic accuracy, wonderful dialog, great plots, and detailed characters is Georgette Heyer. Her books are being reprinted and are truly wonderful reads.