Is it possible to have no overbite or underbite?

Yes, but: You actually want a very slight overbite. If teeth are edge to edge they will wear the teeth over time.

An edge to edge bite: The absence of either an overbite(normal or excessive) or an underbite describes an edge to edge relationship of the incisors. This relationship can be traumatic to the incisors, depending upon their degree of engagement , as well as on the tmj's (temporomandibular joints), due to the lack of incisal guidance.

Yes-see below: When upper and lower front teeth touch on their edges with no 'overlap' there is no over or under bite. This can happen by teeth out of place or an upper to lower jaw mismatch. Upper teeth should normally be forward of the lowers so that food biting takes place like scissors cut not like a chopping block.

Sure: Overbite means your lower teeth are up too far (or your upper teeth are down too far.) if they are just right, it means you have no overbite. Underbite means you lower teeth are in front of your upper teeth. If your upper teeth are in front of your lower teeth, you do not have an underbite.

Possible: Front teeth should overlap each other about 2mm both vertically (overbite) and horizontally (overrate). Anything other than a normal relationship is problematic and may be indicative of either a tooth-size discrepancy or malrelationships of the side teeth and/or jaws. Ask your Dentist if an Orthodontic consultation is in order.

End to end bite: The end to end bite is not a natural, "normal" bite, but there are several people with such a bite. It is not the most functional, healthy type of bite, but correction may involve orthodontics and oral surgery. You may want more than one opinion if you consider any treatment. Unfortunately an end to end bite is like walking on your tip toes all the time, which can create some TMJ/TMD issues.