Sometimes it’s nearly impossible to get the perfect photograph in a popular tourist location, without having gobs of people crossing into view. Wired’s how-to wiki has a useful entry on removing these bipedal obstructions from your travel photos.
The trick is to use a tripod to take a number of duplicate photos. Each photo should have some portion of the subject unobstructed, and if you take enough of them, you should have every portion of the subject represented in at least on of the files. If you use the same settings and frame all of the shots exactly alike (hence the tripod), it’s then just a simple matter of stacking all of the versions on top of each other and cutting out the tourist portion of each layer. All that will remain is the intended subject, and assuming you were careful to capture enough images, there won’t be any gaps left behind.
There are a lot of things that can make it easier to achieve good results with this method. Simply, the closer each of the images are to each other, the less visual artifacts you’ll have to deal with in post processing. Using a tripod to keep the framing stable, enabling manual focus, fixing the exposure settings, and taking the photos as close to the same time of day as possible will go a long way in making your post-travel photo reconstruction efforts less of a chore.