First: of course! Many do-it-yourself designers are blind to how obscure they've made exactly those buttons/links they most want people to click. It's easy to make a design that's natural and intuitive for yourself; for everyone else you have to test, or (second-best) use well-worn rules of thumb that others have tested.
Second: I suspect there's still room for improvement. White text on a solid brown rounded rectangle with slight drop-shadow gives a fair button/click-here hint, but is still not as strong as I've seen elsewhere.
Some companies who thrive by download rates (Adobe Flash, Apple ITunes, Skype) use brighter colored buttons, with a faint gradient, and possibly a down-arrow icon, mouseover highlighting, or a contrasting border.
You may also want to compare against a large text 'download [filename] now' link with strong hyperlink hints (blue, underlined).
Jakob Nielsen's Useit.com has lots of good, test-discovered guidelines in general. Though not specifically aimed at 'download'/'purchase now' buttons, all of the "Top 10 Mistakes" articles are worth reviewing. You could start at:
Jakob's "Law of Web User Experience", which is "users spend most of their time on other websites", is also a good guide. Study and mimic the best practices of other more popular sites that use the same sort of 'download'/'purchase'/'add to cart' button. They've done the testing and trained the users; novelty usually confuses.
1) He mentioned releasing a new version of the software at the same time. It is almost a rule that announcing new releases in blogs or sending customers a newsletter always makes a noticeable increase in visits to your page, including downloads of your app.
2) Lots of shareware trackers check an industry-standard file on the app's web site to learn about updates, drawing more attention to apps that are "new" or "updated."
3) With a software product, as with web apps, the goal of your site is to get the person to use your product, if not pay for it outright. Therefore, there should be an actionable prompt to download the software on every page (though not always in the form of a big red button, of course.) As most visitors leave the homepage of most web sites they've never been to before right away, there should be something for them to do.
I'm not convinced that this substantially increases the installation and especially the usage of the application.
I bet many people click the download button so that it can download before they figure out whether they even want it. I do that all the time. If I read more and I decide I want to install the software, it is already on my desktop waiting for me. If I read more and decide it won't work, I just delete it.
Part of me hates the fact that this works so well. But then again I think "in your face" is actually OK in this case, because you're making it easier for people to find what they're actually looking for.
This is a whole lot more annoying when websites do it with stuff that you're not interested in, like ads.
I believe a large-ish download icon is good user interface. I know if I go to a web page discussing a program and desire to download it, if I don't see a button (or the word "Download" in large, bold text), I immediately switch into find-the-download-page mode. Since Firefox this has meant typing "/download" into the window, which has mitigated a lot of the need for a button, I guess. :)
When presented by themselves, yes. When there is some pretext leading me to the point that I want to click a big shiny "download"/"sign up"/"take a tour" button -- and then POOF, it's right there under my mouse -- I think that is sometimes helpful.