Four times a night on Monday through Thursday, two times on Friday and Sunday.
In the early half of The New '10s, it ran 3 hours per night weekdays on TBS, until the network got rights to re-runs of The Big Bang Theory, which caused it to only air on Mondays.
From 2009 through 2015, TBS would play a big marathon of Family Guy showing every single episode the week after Christmas. As soon as the annual A Christmas Story marathon came to a close, TBS viewers could expect to see nothing but animation that entire week. During the last two years of the marathon, other Seth MacFarlane shows would be played alongside the Family Guy episodes.
In New York City during the early half of The New '10s, between the FOX, TBS, Adult Swim and syndicated airings (the CW station WPIX being a notable one, airing it three times in the morning, twice at noon and two or four times at night), the show could air anywhere from twelve to eighteen times a day, which meant it was aired more frequently than other popular shows at the time. Now it's been cut down to eight times a day, after WPIX screwed the show over for The Big Bang Theory, airing it at 2:30AM in the morning.
The Cleveland Show has certainly become a network favorite. Not to the same extent as The Simpsons or Family Guy, but it did receive two full seasons before airing a single episode, and it is more heavily promoted than a certain other MacFarlane show.
As of Fall 2011 they're going in the opposite direction. It spent nearly all of 2011-2012 in the 7:30 slot (where viewing levels are erratic at best, and the lead-in is usually a repeat of another show) and is returning to that slot for 2012-2013 while Fox tries Bob's Burgers in the main block. And now it's Seth MacFarlane's first non-live-action show to be axed for good...
Chilean network Canal 13 just lovesThe Simpsons, to the point they will fill any spot they need with it. During the summer, the channel plays Simpsons blocks 2-3 hours long at morning, afternoon, and evening. This roughly sums up eight hours a day of a single show, never mind that they often skip episode credits to save time for adding an extra episode per block. In other words, they can air an entire season in a single day, the only reason they don't being that the episodes are randomly picked for the day. Sometimes, a small block of Futurama episodes airs before the morning Simpsons block. Still, it's not like they actually cut all the episodes in half just to accommodate for the prime time soaps. Oh wait, they totally did.
Some time ago, in 2009 actually, a new executive at Canal 13 (Vasco Moulián, if you're interested) developed a "flexible grid", where he would cut, extend, and change the programming according to the ratings — in real time, so if a show was running low on ratings it would be cut and replaced with something else on the spot, without a chance to tell anyone beforehand. And if there was any gap in the grid, we got The Simpsons. The backlash was so big that it cost him his job (despite getting Canal 13 from third to first place in viewership; make of that what you will). Afterward, the flexible grid was quietly put under the rug.
Outside of reality shows, Australia's Channel Ten also loves The Simpsons. It has pretty much always kept its daily 6:00 PM slot note This is when all the other networks are airing the nightly news. Ten air theirs at 5:00. since forever and will often show a couple of other episodes at other times. Mostly on Wednesdays where another two or three episodes might air after 7:30.
That is, until they decided to try a two and a half hour news block consisting of their aforementioned 5pm broadcast, followed by two new half-hour news based programs, and concluding with the already established 7pm Project. The Simpsons have been shunted onto Ten's secondary channel, 11, where it is shown at least twice during primetime, often being split/followed/alternated by episodes of Futurama as part of an 'animation fixation' block.
Channel 4 also has The Simpsons at 6:00 PM over here in the UK, when BBC One and ITV are showing the news.
FOX 8, the Australian Fox channel, shows The Simpsons several times a day and airs nothing but The Simpsons on Saturday and Sunday mornings. During the 2006 Commonwealth Games they showed nothing but the Simpsons for 10 DAYS! To add to that, they show up to 6 hour marathons all the time. School holidays, summer holidays, back to school, Christmas, Easter... pretty much any excuse to show Simpsons marathons.
The irony of all this is that, over in the US at least, there have been rumors of a Simpsonschannel in the works. Today, that channel exists: it's called FXX.
Back when they had Fox Kids, Tiny Toon Adventures counted as this trope. It was promoted heavily when it came over from First-Run Syndication for one season, and given a spin-off of sorts (the Plucky Duck show). Even after new episodes were no longer airing, Tiny Toons clips were included prominently among clips from other newer shows in Fox Kids promos (such as this one).
They also loved Bobby's World, as it stayed on the longest out of the shows on the initial line-up.
Spanish channel Antena 3 has been broadcasing two episodes of The Simpsons everyday for almost fifteen years. There was a time that they broadcasted three daily episodes on weekdays and four or even five on weekends. Its sister channel Neox currently broadcasts three episodes every night plus a marathon running every Tuesday, but two years ago broadcasted five episodes every day. It's so Adored by the Network that Antena 3 has bought the rights to broadcast The Simpsons FOREVER.
The FXX channel decided to run an "Every Simpsons Ever" marathon in late August 2014. Exactly What It Says on the Tin, they aired a non-stop twelve and a half day marathon of all 552 episodes that had aired at that point and the movie. After it ended, the network decided to program 4 hour blocks of The Simpsons for Monday, Tuesday, Thursday, Friday, and Saturday nights during the primetime slots. They advertise it by saying "the Every Simpsons Ever marathon continues... forever". Entirely justified, as the network's ratings skyrocketed during those 12 days. Unlike most shows that get this kind of treatment, The Simpsons has more than enough episodes to sustain such a thing.
In digital terms, the FX Now app also has "Every Simpsons Ever', so basically you can watch the whole marathon at anytime you'd like.
History repeats itself on Thanksgiving of 2016, when FXX decided to start another marathon of ALL 600 episodes called the #The Simpsons 600, which will run for 300 hours, which is 13 DAYS.
One TV station in California (Los Angeles area) aired The Simpsons every day for at least four hours in 2012 until The Big Bang Theory came along.