Dentist Logos -
These logos work well because they are clean cut and simple, they have teeth on them so it can be easily recognised as a dentist. The use of color is interesting - most of the ones i seen are different shades of blue - i think that would be because a lot of people are scared to go to a dentist so a calming, relaxing colour on the logo of the dentist would make people more comforted than a logo that was red or black.
Gymnasium Logos -
These logos appear to work because they are bold, show pictures of fit people and also gym equipment, so you know what type of business it is just by looking at the logo.
Florist Logos -
These logos work because the colours are eye catching, they have the product they sell pictured in the logo somewhere (a flower), they are soft, sweet, fun and simple.