Standard Height Tables:
Pros: Standard Height Tables are more common and therefore available in more sizes, designs and finishes than counter height tables. Most people find standard height tables are more comfortable to sit at because their feet touch the ground while they are seated. They are also a better height for disabled people, as a counter height table is too tall for a person who sits in a wheelchair. Finally, standard height tables are considered more formal than counter height tables and might be a better fit into a formal themed dining area because of this.
Counter Height Tables:
A Counter Height Table, with its additional height can be used near the kitchen for an additional prep area. Counter Height Tables are also considered more casual, and make it easier to converse with others standing in the room. They give the illusion of taking up less space than a lower table and can work well in small areas. Because Counter Height Tables are considered less formal, they create a more relaxed, casual atmosphere than sitting at a lower, more formal table.
Bar Height Tables:
These tables are typically around 40"-42" in height. Therefore, the bar stools are in the 28"-30" range. Bar height furniture is most commonly used with home bars but can also be found in some pub sets and counter set ups. These tables often be mistaken for Counter Height Tables and vice-a-versa. The advantages of a Bar Height Table are the same as Counter Height Table but even more-so. They are extreemly causual, as the difference between standing and sitting is even more blurred. They are tall and thin, and can fit in places where no traditional table could. Bar Height tables are perfect for creating casual seating in a relaxed attmosphere.
Additional Reading at ehow.com:
Standard Height vs Counter Height Dining Tables