One-pixel transparent gifs may be a web developer's crutch, or they may not be. One thing they often are, however, is a subtle way of eroding your privacy. Because the HTTP spec (the thing that defines how web pages are accessed and transmitted) allows a site to attach cookies to images, users of a website may be transmitting all of their browsing information not just to the website they intend to browse, but also, unknowingly, to a third party that only serves up one-pixel transparent gifs. This way of tracking people was, for a time, so common that these were referred to as web bugs.
Whole services have been built on the idea that a person won't notice a one-pixel transparent gif. If you want to track whether a person has opened and read your email, then there exist (or at least used to exist) services that will give you an image to put in your html email. If that image ever gets downloaded, then your email's recipient has most likely read your message. This tactic is also frequently used by spammers in order to figure out which email addresses are valid. They put pictures at unique URLs for each email they send out, and all the images that get downloaded correspond to email addresses that people actually read.
Because when your computer downloads an image it also sends a whole host of other data to the server it is requesting the image from, they also know what download and display tool you are using, allowing them to specifically target viruses and trojans towards only the people who are infectable.
All of the tactics that use email can be foiled if you choose not to display remote images in your email reader, or if you don't use HTML email at all. This latter is actually recommended, as your text is what is important, not the font you use. Despite the relative ease with which these attacks can be rendered useless, their prevalence in the early days of the web and HTML email has led to a distaste for one-pixel transparent gifs amongst privacy advocates. Much adblocking software will block them, and their presence in an email will often trigger spam warnings.
If you are using them with the best of intentions, and only for spacing and the like, these little dots should be used with care. The abuse of these in the early days of the web has meant that web browsers and privacy filters prevent them from being dealt with in a consistent manner across all browsers. If your layout depends on people doing something that has historically been bad for them, you might want to fix that.