Connecticut Limo has been offering transportation from New Haven to the area bus and plane terminals for years.
They offer personalized limo service as well as shuttle/van stops. They offer 24 hour service, and have a set schedule that they operate on for non-individualized service. Private rides are available, and can be quite expensive.
The van's and buses that they use appear well kept. The attitudes of the driver's are on par -- you'll get some on good days and some on bad.
Their prices are somewhat expensive, but you are paying for a specialized service. Because they are the only shuttle service in Connecticut, they curb that market well.
Located near Sports Haven plaza, parking is not a problem.