This isn't a problem unique to SAHD's, but its one you're going to have to deal with. Television. How much of it? And for that matter, how much computer time, playstation time, and whatever else is out there that isn't akin to white-water rafting followed by a ten-mile hike in full packs.
People like to complain about how much TV kids watch, and what they watch, but who's in charge of the TV? Hmmm? Helloooo? Yeah, you are, and as tempting as it is to just park the little beasties there as long as they want, we all know we really shouldn't do that.
We decided that our son can have two hours, total TV and computer time in a day. How he splits it up is up to him, but that's all he gets. There are exceptions for special movie nights, colds and injuries, rainy days, sick dads, etc, but the point is that there is a limit.
And in addition to time limits, there are limits on what he can watch. Well, no duh, we aren't going to let him check out Naughty Night Nurses or pretty much anything on Spike TV, but even kids programming can be exceptionally lame or even offensive to my wife and I. And very little of it is educational in any sense of the term. SpongeBob is reasonably inoffensive to me, but its just cotton candy. And our view is, if we limit his time on the TV, what he does watch should be of some redeeming value.
It gets trickier as they get older. As insipid as it is, Barney (is that still on) and its cousins do fairly well at hammering home the idea that you should be nice, share, etc. But these shows tend to be for the really younger crowd, from 2-4. You have to move on, and find something else that might engage their minds and be entertaining. We're not trying to run a joyless Gulag here, after all.
PBS kids shows (once you are safely past the Barney stage) and the Disney Channel are pretty safe if not always terribly inspired. A lot of the Nickolodean shows are actively good, like Blues Clues and Dora the Explorer.
Other shows that I found really good in the past, in that he liked them and they actually taught you something besides "be nice to people" were shows like Stanley on Disney, Liberty's Kids, now syndicated on the WB (previously on PBS), the Magic School Bus (also a way cool set of books. Note there are two sets, the originals, plus newer ones based on TV show episodes) running on The Learning Channel, and right now, CyberChase on PBS.
Stanley is about a 6-year old who loves animals, and each episode contains two short stories where Stanley learns something about life via animals.
Liberty's Kids is a totally cool show covering the American Revolutionary War, from the Boston Tea Party through the creation of the Constitution. Its seen mainly through the eyes of three (miraculously non-aging) kids who are apprentice newspaper reports for Ben Franklins Pennsylvania gazette. It strikes a nice balance between being rah-rah and noting the occasional warts of the Americans.
The Magic School Bus (theme song sung by Little Richard -- no joke) is about the science adventures of a class and their wacky teacher Ms. Frizzle. They get shrunk, go back in time, inside volcanoes, etc. learning about all sorts of science stuff along the way.
Cyberchase is a a show about three kids who work to foil the schemes on the evil Hacker to take over the cyberworld. Along the way, it does a cool job teaching math and logic concepts.
As I noted earlier, kids grow.
Some of this stuff (the Nick shows especially) are not geared for a 6-year old. Jacob finds them boring and babyish. Perhaps in some cases its just because he's seen every episode ten times. Even little kids have their limits when it comes to repetition.
Timing is a bit of an issue as well. Magic School Bus comes on at 7:35AM CST. Jake is on the bus at 7:15. School starts at around 8AM all over the state of Texas. MSB is a great show, but who's watching? The Mountain and Pacific Time zones, I suppose, but those of us further east are stuck unless we Tivo it or manage to work the VCR. Other of the Nick shows come on later, geared to younger stay-at-home kids.
At our house these days, we do CyberChase at 6AM, then follow it with part of a VCR or DVD rented from Blockbuster for the remaining half-hour. We let him watch these things while eating breakfast, getting dressed, and generally emerging from the early-morning coma that characterizes my wife's side of the family (she jump-starts the process by fixing a double-size mug of coffee that probably violates certain FDA regulations) and also affects me to a lesser extent. Without the tube to provide him a bit of groggy focus, I truly think he would fall right back to sleep, face-first into his organic-wheat waffles. And we're putting him to be about as early as we can already. When he gets home from school, he typically hits it again until time's up or his buddy from across the street comes over (TV and/or the computer always goes off if someone comes to play. That rule is iron-clad), and depending on homework, etc.
So anyway, think about your kids TV, give my shows a try, feel free to suggest some others, and remember that, when in doubt, Scooby Doo is eternal.