I'm curious how well the window shrink wrap really works. I moved into an older house (1927) in Lincoln, Nebraska, this summer. It's all single pane windows with a window screen and a storm window, as well. We have about 20 windows, so I'm estimating a cost for shrinkwrapping to be about $50-$100 with a couple hours of labor, too. I also just think the plastic shrinkwrap looks a little ugly, but if it'll save me more than it costs to install, it might be worth it. I've found some research just saying to replace the windows, but that's not feasible right now.
You will almost certainly save $100 on your heating costs by using film, assuming you install it well and stop drafts through the window seals. It may also make the home feel more comfortable, which can be the primary benefit.
Also, properly installed film is virtually invisible. You hardly know it's there.
In my former home here in Minnesota we put the tape on the face of the casing, applied the film, shrunk it, then trimmed the edges close to the tape. My wife usually did the job and could do it in a few hours. It was a no-brainer for us even with storm windows over the single-pane double-hung units from the 1950s.
Film in Nebraska would likely be worth it, at least for the worst offenders in terms of drafts.
A tight storm window can boost a single-pane's R-value from 0.9 to about 2.0, which is actually comparable to many double pane windows. Coated storm windows can also drastically lower emissivity (by 75%) over plain glass ones, which helps a lot aside from R-values. Those upgrades will pay for themselves, and reduce the need for additional seasonal measures like film.
An easy and cheap way to keep the house warmer and more efficient is to stop air leaks around windows; most importantly the frame seat and between double-hung panes. For this, you can use a variety of cheap materials, including ready-made products. Caulk around the frame, around the storm window seat, and anywhere else that can take caulk and flickers a flame held close-by. If you can get everything air-tight you likely won't need film.
Get creative. My grandma always used the leftover loop half from a long strip of hook and loop (velcro) to tighten up the seal between frames. I fixed my old mudroom window by injecting hot glue between the panes to build-up the face, using wax paper in front of the top pane so you can't see any glue through the bottom pane when open. You can even simply cram soggy toilet paper into the cracks with a credit card, a trick from my dorm days, which works very well until the window's opened next spring.
No matter what you do, the big money is in stopping drafts. If you have no drafts, film doesn't add a whole lot of value. If you see attached film bow or cave, it means you have leaky windows, which should get fixed regardless of using film or not. I would patch things up air-tight, and if needed, apply film only where still needed.
Air has pretty good insulation value if you can stop it from convecting. If it convects, it transfers heat fairly efficiently.
Fiberglass and rock-wool matt rely on this - the point of the strands is to create boundary-layer effects that prevent the air from circulating. That's why compressing fiberglass makes it insulate worse.
Too wide a gap between window panes will allow convection. They find under 1" is a good gap.
So when applying films, that's the target to aim for. If it's your own house, feel free to get some 1x1 square stock (3/4 square, really) and build yourself some spacers.
Also, more layers help more.
Also, make sure your windows are tip-top and properly maintained. For instance I am very familiar with "drafty" Victorian windows. Turns out, they're not supposed to be that drafty, and aren't if properly maintained. But things like the brass edge seals and top/bottom felts tend to be deleted by landlords during maintenance.
Growing up in Iowa in the 80's and 90's, we would put plastic on our windows every year. I'm pretty sure they were all single pane windows, too, as it was an older farmhouse.
As a kid, I don't know how much it helped with the cost of heating, but I know that the rooms where we didn't do this were often unlivable. Many of these windows, especially the old wood frame ones, had nasty gaps where the seals were damaged or missing, so there were pretty good breezes coming through. Because we didn't have AC, we sometimes left this plastic on during the summer months.
We eventually added caulk where possible and fixed other problems when we could.
The real solution is to replace the old windows with new, insulated windows. You don't have to do it all at once. Replacing 1-3 windows a year will help a lot. You can either start with the main living rooms first or replace the worse windows first. Yes, this costs a lot of money, but it will pay off later. It'll help with cooling costs, too, so you'll be getting year round protection. Not only will it prevent air leaks, but it'll help keep UV from getting through, as some windows have a coating, tinting, or polarization to help with that.
Southern Michigan here. It makes a huge difference on single pane windows and a somewhat noticeable difference on newly-installed, well-caulked double-paned windows. On windows that we don't open, we tend to just leave it in place all year round (like the single-paned windows behind my boss's desk at work). On windows we like to open, we end up forgetting about it most years (well-caulked 15-year-old-now double-paned windows).
When we were doing construction and weren't using part of the house, plastic sheets hanging in doorways makes a noticeable difference as well.
Thick curtains made out of say... blanket material can look nice if you're into it, and they add a lot to the insulation. You can stack the effects with cling-wrap, and the blanket curtains can be made larger than the window itself if you're getting a draft around the edges. Only downside is that you don't get the heat of the sun coming in, and of course you lose the natural lighting. I think we get more use out of the cling-wrap, though.