This answer depends quite a bit on when in the 1940s you mean. When you hit 1949, while only 6% of households had a TV, 44% of people have seen one, and most people are expecting by that time for television to eventually supplant radio. Reverse back just a little bit to 1946 and you have televisions numbering only in the thousands in the entire country and many Americans still haven't even heard of television.

Based on your question I feel like you're aiming more for the 1946 experience rather than the 1949 one, so I'll focus on that. Let me just mention the prior years including the 1930s do have some eventful times as well; for example, New York City in the early 30s had an experimental station (W2XAB) with about 3 hours of programming in the evening. Here's their listing for August 21, 1931. Each program goes for 15 minutes, except the play which runs for 30:

Harry Swan, specialties.

Poet's Favorites.

Play, "Hawaiian Shadows".

"Looking at Television," Charles E. Butterfield.

Television demonstration by Lighthouse for the Blind.

Stanley Davis, songs.

Boswell Sisters.

Connie Boswell, songs.

"Television Hints for Swimmers," Charles Speer.

Ruth Perrot, songs.

Barbara, Maurel, contralto.

Before anyone asks, I have no idea if Hints for Swimmers is literally about the sport/activity or something else, and Harry Swan was a variety act; he was also on a radio show called The Nit Wit Hour where he did both singing and acting as "Professor R. U. Musclebound".

In 1949 you had -- in addition to news and sports broadcasts, like Meet the Press which is still going -- relatively recognizable shows such as Howdy Doody, The Goldbergs, Ripley's Believe it or Not, The Lone Ranger, and Candid Camera. (The Goldbergs incidentically also were around in 1931, just in radio format.) Oh, and Captain Video and His Video Rangers launched, with secret decoder rings.

But let's do 1946. Importantly, 1946 was the first year there was a "television season".

Your networks were NBC and DuMont; CBS had just one station. ABC and others hadn't bothered to get into TV yet. Broadcasts went from 7 pm to 10:30 pm, with a fair amount filled by "local programming". (The short reason why CBS only had one station is there was a "standards war" over color television formats, and CBS wanted their standard used rather than the RCA standard, so they delayed national rollout and ended up losing 4 years over their competitors. ABC just didn't have the money.)

NBC shows:

Face to Face: A cartoonist draws someone they've never seen before based on a description.

Geographically Speaking: Narrated home movies of travel. Sponsored by Bristol-Myers.

I Love to Eat: The first TV cooking show, hosted by James Beard. Yes, the same one as the Beard Awards. Sponsored by Borden.

You Are An Artist: Teaching how to draw, hosted by Jon Gnagy. Unlike many of the things listed here, you can watch an approximation: here's a show from the same artist made in the 1950s.

Let's Rhumba: Teaching Latin dance.

Gillette Cavalcade of Sports: Usually boxing.

Just to be clear, while boxing was the only "regular" feature, other sports did make it on television -- the first ice hockey broadcast, for instance, was 1940, and the first professional wrestling broadcast was 1941. However, boxing was definitely the dominant TV sport, and the first heavyweight boxing title match was broadcast in 1946 (Joe Louis and Billy Conn, seen by over a hundred thousand people).

Essentially, boxing was much cheaper to produce televised: it was indoors, in a small self-contained area, and it could attract a large male audience to taverns (as home televisions were quite rare still).

DuMont shows:

Play the Game: Charades.

Serving Through Science: Moderated discussions and short films produced by the Encyclopedia Britannica and sponsored by U.S. Rubber.

Faraway Hill: A soap opera. (There were plenty on radio, so not a surprise, but this was the first on television. The scripts are privately owned, and this was before anything got recorded, so we unfortunately don't know many details.) Here's a clip from a review in Billboard magazine:

Story concerns a Park Avenue gal who goes to visit her country shirttail relations and unhappily discovers that they’re not in the 400. While on the farm she falls in love with the hired man who in turn falls in love with the farmer’s daughter. Up to this point, she has tried every conceivable trick known to the fem trade to win her man–but to no avail. And she’ll proably go on trying as long as Caples foots the bill.

(Caples is the company that funded the show.)

King Cole's Birthday Party: The actual birthday party of a child. Sponsored by the Jay Day Dress Company.

Their schedule also lists "Western movie" for an hour every Friday.

CBS

I don't have as many of their shows offhand but I'd like to mention You Be the Judge, a game show with a real-life court case re-enacted and three guests "judge" -- the guest who got closest won a prize. The cases weren't quite murder; from a Billboard review:

In case you are interested, if you ever find a pearl in a restaurant, it belongs to the restaurant owner, not to you, under the laws of Connecticut.

Missus' Goes-A-Shopping was a female-contestants-only gameshow (the audience was also only women) and was broadcast from various Manhattan supermarkets with stunts and trivia.

Advertisers

Since you asked, it should be clear by my various mentions: it was mostly a mono-sponsor universe. You had one company -- say, Gillette -- sponsoring one particular program, and of course that means they can mention Gillette all over the intro. You can watch a little to get the idea.

...

There are some very nice pictures of WX2AB at the Early Television Museum.

Brooks, T., & Marsh, E. F. (2009). The complete directory to prime time network and cable TV shows, 1946-present. Ballantine Books.

LaFollette, M. C. (2013). Science on American television: A history. University of Chicago Press.

Neal-Lunsford, J. (1992). Sport in the Land of Television: The Use of Sport in Network Prime-Time Schedules 1946-50. Journal of Sport History, 19(1), 56-76.