One fairly well-kept secret—low-emissivity (low-e) storm windows—lies somewhere between these two options. They aren't the simple, low-cost, do-it-yourself option that Jen spoke of. But they are a less expensive option than the replacement windows I wrote about.
I'm an avid reader and subscriber to the Environmental Building News newsletter. Alex Wilson, the newsletter founder and Executive Editor, wrote an article entitled "Should I replace my windows?" in the Brattleboro Reformer (unfortunately, the article is no longer publicly available online, that I could find). Alex is one of the world's experts on green building materials, so I'm always glad to see what he has to say. One option he described is adding low-e storm windows if your existing single-pane windows are in reasonable condition and replacing the sash isn't an option. He added that they aren't an option with casement or awning windows. You may even consider adding storm windows to existing double-pane windows, though the savings will not be as great as with single-pane windows.
Storm windows are viable options if replacement windows are outside your budget, or you're trying to maintain the look of an historical building. Adding exterior storms also forgoes disruption inside the house during installation. Alex recommends outside-mounted, high-quality, triple-track, aluminum-framed storm windows, with low-e glass to boost performance, for Vermont where he lives. He emphasizes that quality is important, since they get a lot of wear-and-tear; triple-track means storms contain an integral screen.
There are two main types of low-emissivity coatings: soft-coat and hard-coat. The former needs to be well sealed, otherwise it will degrade. It's not an option on single-pane glazing, such as storms. Hard-coat low-e is much more forgiving and can be used on single glazing; I just wasn't aware that you can obtain low-e storms. Low-e storm windows are custom manufactured to fit your existing windows, so it makes sense that you should be able to specify low-e glazing.
Low-e coatings are one of the technologies that have improved the energy efficiency of windows. Will a low-e coating make a difference on storm windows? According to one New England-based window manufacturer, a generic double-hung wood window installed with their clear glazing storm window had a U-factor of 0.45; the same window with their identical storm window with a low-e coating measured a much higher level of energy efficiency, having a U-factor of 0.35. (Lower U-factor means higher R-value, which equals higher energy efficiency.)
Efficient storm windows cost approximately half the cost of energy-efficient replacement windows, uninstalled. Check with your contractor for total installed costs.