1. Don't let the rules stifle your creativity
Most enthusiast photographers know at least some basic composition rules, for example rule of thirds or using foreground interest in landscapes, but you shouldn't let these become a straightjacket. Landscape photography in particular suffers from a 'by the numbers' approach, so don't ALWAYS place a big boulder in the foreground to lead in the eye. Your picture my be technically competent but it lacks individuality.
2. Be careful with clutter
Background distractions are the bane of any serious photographer and is a particular issue in travel and documentary/street photography, as clutter is often beyond your control. The point of avoiding clutter is not to get 'perfect' shots, but to make sure your viewer's attention is focussed on your main subject. Cloning out stray heads and beer bottles in Photoshop can be a pain, and it's even harder in Lightroom, so take an extra couple of seconds to check for distractions before you take the shot. With more static subjects, you can lock autofocus by half-pressing the shutter button, then recompose for a cleaner background. Another good tip is to use a wider aperture (or long telephoto lens) to reduce depth of field and blur out distractions.
3. Give moving objects space
Panning is hard to get right, so don't lessen the impact of a great pan with too tight a crop. Panning shots work best when the moving object has some space to move into (an exception is maybe a motorcyclist cranked over for a very tight bend). Crop in too close on a typical panning shot and it just feels too 'tight'.
4. Don't overuse vignetting
A classic technique in portraiture is to deliberately darken the corners to focus attention on the main subject. It's a great technique, and takes literally seconds in Lightroom. Use it sparingly though; as with the dreaded foreground boulder in landscapes, if all your portraits are vignette in the same heavy-handed way, your work looks very formulaic.
5. Try to keep lines straight
Wonky horizons and 'converging verticals' on buildings – where the edges lean in or converge towards the roof or sky – are giveaway rookie errors. Fixing wonky horizons or lines takes seconds in software (Lightroom's crop tool is much easier to use than Photoshop CS). The best way to avoid converging verticals is to use a tilt and shift lens, but these are very expensive. Again you can fix it in software, or try using a prime lens, such as a 50mm, for your building shots; there tends to be less distortion than with zooms.