Sure! It has probably happened several times in the last few thousand years. It is very rare, and is strictly a matter of timing since Mercury goes round the sun every 88 days, and Pluto goes around every 240 years or so. Clearly the outer, slow moving planets are the most critical in deciding when this will happen.
As for what would happen, well...if you are looking for some cataclysmic event, none has ever been uncovered in the historical of geological record. The only conceivable effect would be gravitational, and the combined gravity of all the planets upon the earth is almost entirely dominated by the influence of Jupiter. There might be a measurable enhancement to earth's water tides, but this effect would be at the millimeter-level and not actually detectable.