Adding a shadow effect to a Logo Design can help to give the design an added feel of depth but many people like to over do this amount of depth by adding heavy drop shadows to a logo. There is not really a right or wrong way to design a logo but using heavy drop shadows often gives a logo a dated and amateur feel. This is not to say that a little shadow does not work as there are many examples of logo design where this technique works well but the point to keep in mind is that if you would like to add a shadow to your logo try not to over do it.
Another good reason not to use heavy drop shadows is that when the logo is printed the results can look quite mucky. Printing is fine for subtle drop shadows but very heavy shadows can reproduce in printed forms with unexpected and unwanted results.
The above example shows two logos, the first has a very heavy drop shadow while the other has a more subtle shadow that works to give the design a little added depth without over doing it.