On a winter night in 1981, Karen Cabic and Ed Babington were each at home in their suburban apartments watching a television show about video dating.

Both were divorced, and both had the same thought: Hey, this is worth a try.

Cabic, who worked in the Patent and Trademark Office, lived with her young daughter. Being 37, she said, "was about the worst. The worst age for meeting people, for starting new relationships."

Babington, also 37, was a civilian Naval worker and twice divorced. While living in Mississippi, he had tried meeting women in singles bars, but gave up in frustration. "In bars, you don't know what the woman's intent is, and sometimes, I think, she doesn't know either."

Shortly after the television show, Babington and Cabic came into town to record videotapes of themselves at The Georgetown Connection, one of two video dating services in Washington.

Their first date, lo and behold, was with each other.

"February 10, 1981," declares Karen Cabic (now Babington), beaming, sitting in the living room of the couple's posh Springfield town house. It was a dinner date, "comfortable." A few days later, Ed took Karen and her daughter out to the Ice Capades, and Karen knew a relationship was in store. They were married in October.

"I had an initial hesitancy because of the stigma about dating clubs," says Karen Babington. "You know, friends looking at you funny. But it's hard to meet people these days, especially if you're in your late thirties or forties, and you have a child. I think they're starting to serve a real function in our society."

Dating services, once considered the domain of strike-out kings and Miss Lonelyhearts, are prospering, with a clientele that tends to be professional, attractive and mid-30ish (though the range is from teens to the elderly). And, if the videotapes at The Georgetown Connection are any indication, surprisingly self-assured.

"These aren't losers, you understand," says Joan Hendrickson, the indefatigable owner of the service. "On the contrary, these are people who are confident and willing to take a risk. You've got to take a risk to put yourself on videotape, to shell out that much money."

How much, exactly, is one expected to shell?

In this case, $350. That's for half a year's worth of dates, a fee that, among other things, "guarantees that the people in the service are serious," according to Hendrickson. Her Georgetown Connection recently celebrated its 70th marriage (since its inception in 1977).

"What the dating services do," maintains Hendrickson, 49, "is provide a small-town network that simply doesn't exist anymore."

But, lest $350 seem extravagant for joining such a network, consider the options.

At the Georgetown Exchange, you can land a date within a few days, for only a dollar and the cost of a stamp.

Queen of Hearts, an intermediate-priced matchmaker, offers a year of dates for $52.

And, if you're afflicted with herpes, there is Today For Singles, Inc., a new dating service catering exclusively to herpetics and offering three dates for $15.

"The dating service business is definitely snowballing right now," says Esta Lee Hoffman, owner of Queen of Hearts. "There are all kinds of interesting singles out there and they need a way to meet. They need to get in touch with people who have similar backgrounds. It's not something that just happens."

Hoffman, 43, started her service ("my hobby, in 1980 because "I was having trouble meeting people, and knew I wasn't the only one."

She lists respectability as the biggest change she's seen in her three years as a matchmaker. People no longer grin when she mentions it; they seem interested.

Although she had trouble advertising her service at first, now even religious papers take ads. "They sense that it's a good thing, I guess."

If the needs of singles are becoming more recognized, it may be because there are so many out there: 49.2 percent of the D.C. metropolitan area and 42.7 nationally are single (age 15 or over, never married, separated, divorced or widowed). The U.S. Census projects that half of the households in the country will be single by the year 1990, a situation that can make it easier to meet people, but harder to make friends.

"People today are busier and more selective," says Hendrickson. "Also, there's more displacement. A dating service takes the randomness out of meeting someone. It saves time. People want the filtering process done beforehand."

But where is all of this leading us? And what is it doing to the traditional notions of romance and courtship?

Dating, responds Chris Styger, 35, a co-owner of the Georgetown Exchange, is "after all, a matter of percentages. You have a better percentage for compatibility with a match than you do with someone you meet in a bar, or on the street." His business, he says, attracts a wide mix of customers, including members of the CIA. He predicts that dating services will soon become the way most of us meet our mates.

Which isn't to say that marriage is the sole purpose of dating services.

Some members say they just enjoy the adventure of going out with someone they don't know. Like Pam, 29, a free-lance photographer, who has used area dating services three times in the past year "getting to know people I otherwise would never meet."

She describes herself as "heavy, but shapely. I have to explain that to people who call. I have to let them know I'm not petite or anything. Some men are looking for that, I don't know why."

Each of her dates, she says, has been interesting. "A lot of conversations. I met one guy down at Roy Rogers'. We had a Coke. Another guy I met in the park and we talked for a couple of hours."

Sharon, 31, an editor for a computer firm, also was more interested in talk than romance when she placed a telephone message with The Georgetown Exchange. Of the 58 responses ("I was overwhelmed!"), she chose six, and sent the rest form letters.

The lucky six split the price of a lunch with her. She never saw five of the men again, but the sixth is now a regular companion.

"It's pretty serious," she says. "We might get married."

As interest in dating services has grown, so has the technology being used. Several area services use computers (and those that don't say they expect to move into computer dating soon); two use video recorders, and one is offering "vox response," a system in which a member can call a number and be connected almost immediately with a prospective match. It's a way of guaranteeing privacy, until both parties agree to the date.

Services also have become more specialized. Sue (who prefers not to use her last name) started Singles For Today after finding her own dating opportunities limited because she has herpes. Despite some annoyances ("We get quite a few crank calls, as you might imagine"), the service has grown steadily, and will soon begin putting on parties and dances. One member, she says, commutes from Pennsylvania for his dates.

If there is a trend in the dating service business, it seems to be toward increased efficiency and sophistication. In the future, "people will expect the same advances in dating methods," says Styger, "as in everything else.

"Eventually, I'd like to offer picture phones. For a rental fee, the customer would attach the phone to his or her television set. Members could then talk to each other, and see each other, without having to give out their names or phone numbers."