On cable sometimes or in the case of a duopoly of an OTA station. I.E. There's a lot of cross-promotion between Tribunes FOX 61 and CW affiliate WCCT-TV 20. There's another duopoly in Hartford/New Haven and that's NEXSTAR's WTNH (ABC) News 8 and WCTX (MY Network), but aside from promos for the Yankees games WCTX picks up from NYC, I don't see any other cross-promotion between WTNH and WCTX.
Oh and occasionally CBS will promote something showing on Showtime as they are corporate cousins. And CBS will occasionally promote something on TBS because CBS and the Turner Networks are partners in the NCAA March Madness Tournament.
I have. On cable certainly, and a lot of cross-promoting between co-owned networks, like Fox shows being advertised on FX, etc. HBO also runs ads on other networks. You'd think that the networks wouldn't want to advertise for competition, and the potential to lose audience, but they don't seemed to care anymore.
Remember back in the day, when a star from a show on another network would guest on say - Johnny Carson? Carson would always note,
"The X show airs Thursday night on another network." That ended a long time ago - now they just name the network and the exact time of the show. So I don't think networks worry about that anymore, because there is so much cross-production. For example, I've seen Fox produced shows air on CBS, and vice-versa. CBS now owns
Jeopardy and
Wheel of Fortune, but they generally run on ABC affiliates. And so on...
Not to mention - The Ken Burns Vietnam War series is a big deal, and I'm sure you'll see promotions, interview with Burns, etc. - on all the morning shows, and lots of other places.