The only reason I ever remember Delaware is because of Wayne’s World .
“Or imagine, being magically whisked away to… Delaware. Hi… I’m in… Delaware.”
As an Englishman, I probably couldn’t name all the States anyway, so how would I know which were forgettable? 
But to comment on your examples above:
- New Hampshire is Jed Bartlett’s home State
- Ohio is where Archie Goodwin was born
- presumably Indiana is associated with Indiana Jones
So I guess Nebraska is my ‘least meaningful’.
Delaware and Nebraska. Wyoming’s beautiful in spots (Yellowstone, as has been mentioned) and I’ve always had an irrational fondness for Montana (least densely populated states, IIRC). But Nebraska is just flat and boring. Even more boring than Iowa, in my opinion. If it weren’t for Warren Buffet and college football, I don’t think I’d know a single thing about Nebraska.
I worked with someone who had been a reporter for the Buffalo News who used to regale us with stories of trying to get a comment about something from the governor’s office.
“Buffalo…no, BUFFALO, goddamit! The second-largest city in the state!”
Another vote for Delaware. All I can conjure up about the state is waaaay too many credit card offers stuffing my mailbox years ago (before I signed up for the Do Not Mail List.) Maybe it’s just a really big P.O. Box. With ocean frontage.
Plus that Steven King guy tends to write about it.
Other than the obvious (which should lose points for coming instantly to mind when being asked for the most forgettable 
), I’m going to go ahead and say Missouri. I know it’s allegedly relatively major, but I have no idea what it looks like, what its culture is like, or otherwise what its nature is in any way. Despite how many people live there, I never hear about it in the news or in any other capacity. Sure, it has that arch, but having a strange monument of little-known meaning or provenance doesn’t quite cut it.
But Delaware is where more than 300,000 corporations were incorporated. It’s like the nation’s corporate nursery.
I vote Idaho.
Missouri must be fairly important. One of the major cities has a whole state named after it. And Truman is alleged to have come from the place. Plus we get to blame Cape Girardeau for Rush Limebag.
The Arch has little-known meaning or providence? Really? OK, How about McDonnell Douglas? Ralston Purina? Anheuser Busch? H&R Block? Sprint? 2006 World Series Winning St. Louis Cardinals? Super Bowl XLI winning St. Louis Rams? St. Louis Blues, Kansas City Royals, Kansas City Chiefs? “Meet Me In St. Louis?” Charles Lindbergh? Spirit of St. Louis? Harry S. Truman? Hannibal? Mississippi River? Mark Twain? Louisiana Purchase? Lewis & Clark? Any of this ringing a bell? 
I had absolutely no preconceptions about Wisconsin before I visited it. None. It was a blank spot in my mind that I didn’t know I had. I knew about Milwaukee, of course, but I never connected it with Wisconsin until I went there and passed through it. (“So THIS is where Milwaukee is!”)
I’d say that makes Wisconsin the most forgettable state.
South Carolina or Connecticut - I had to look on a map to remember them.
Michigan isn’t particularly memorable, should be named “Detroit” since that’s the only thing I know about the place.
If the wonderfully sardonic Mr. Clemens could see the Tom-Sawyer-and-Becky-Thatcher-ified mess they’ve made of Hannibal, he’d forget it too. Or possibly he’d write a marvelously fine-tuned 5000 word evisceration of it.
I vote for North Dakota, as it is the only one of the lower 48 I never bothered to go through in my hitch-hiking days.
I’m really from Delaware (born in Wilmington), and live there (in Newark, not Wilmington) now. I like it here, anyway.
edit to fix coding
I’m going to have to say Vermont, as well.
Otherwise, Oklahoma or Montana.
I say South or North Dakota.
Wyoming has Yellowstone and Jackson Hole and the Grand Tetons - so to anyone who’s been there, it’s quite memorable.
Kansas equals flat and wheat; Nebraska (never been through) equals corn; Oklahoma equals not Texas, the Dakotas equal nothing.
There should probably be more monasteries located in the Dakotas.
Fort Sumter?
I think this probably depends on what part of the country (or world) you’re from. I’m from the midwest, so I’m really surprised to see places like Wisconsin, Missouri and Michigan (if for no other reason than it’s the big giant mitten that slaps you across the face whenever you look at a map of the US). People from the east seem to be defending places like Maine and Delaware and Connecticut. But honestly, most of the things describing Maine were all so foreign to me, my eyes just glazed over them when I read them.
Me? I say Montana. No professional sports teams, no college teams that stand out in recent memory. No major cities spring to mind. Can’t think of anyone famous from there. Or anyone non-famous, for that matter. It isn’t the biggest, or the most mentioned in lists like this, has no real monuments or natural wonders. I couldn’t tell you Montana from Wyoming on a blank map of the US (Wyoming has a few things going for it in my eyes: Cheney is from there, it falls last alphabetically and the Matthew Shepherd lynching). No major industries (cars: michigan, beer: wisconsin, potatoes: idaho). It doesn’t border many other states, so your average person probably wouldn’t even have any real reason to drive through it.
Montana, indeed.
Kansas. Possibly Oklahoma. Name one thing about Oklahoma. Wisconsin has cheese, Delaware credit card companies, Nebraska corn, even Idaho has potatoes.
We’re not in Kansas anymore? Good.
Custer’s Last Stand?
Yeah, yeah, if the marvelously sardonic Col. Custer could see…