It is not terribly uncommon to see a stone arch bridge with cracks in various places, including the arch. While certainly meriting a closer inspection, cracks are not always a cause for immediate concern, especially if they have remained unchanged for a long time (see our post on Monitoring Stone Bridges). For those who want to know more about cracks in bridges, we found Safety of Historical Stone Arch Bridges by Dick Proske and Pieter van Gelder an invaluable resource.
Longitudinal Cracks
At least in our local area (southern Kansas), longitudinal cracks seem to be the most common form of cracking found in a stone arch bridge. Longitudinal cracking is generally not overly serious in and of itself, unless it occurs near the outside of the arch, which will be discussed later. Longitudinal cracks in the arch are very likely caused by one section of the arch settling more than the rest of the arch. This could be due to looser-fitting stones in the arch resulting in mild tensile forces in the structure, but the most likely cause is one-sided settlement of the entire bridge. The main concern would be the cause and progress of the settlement. Such settlement could very easily be caused by scour, which is quite serious. However, if the bridge is not being undermined and the crack is not worsening, the situation is likely not serious.
Water Infiltration and Stresses
Longitudinal cracking can occasionally occur for other reasons besides one-sided settlement of a bridge, such as water infiltration deteriorating a section of the arch.

Very wide arch bridges can sometimes suffer from longitudinal cracking due to unequal stresses across the entire arch. As an example, a stone arch bridge with heavy two-lane traffic moving in opposite directions can split in the middle, in effect splitting the two lanes of traffic onto two separate arches.
Serious Longitudinal Cracking
A far more serious form of longitudinal cracking occurs at the upstream and/or downstream ends of the arch directly below the spandrel walls. This type of cracking essentially separates the spandrel walls from the rest of the bridge. This type of cracking can be caused by movement of the spandrel wall itself. While a failing spandrel wall normally moves by itself, it can and does occasionally break off part of the arch below with it in its travels, leading to longitudinal cracking. Longitudinal cracking below the spandrel wall can also quite possibly be due to moisture penetration, as in the case of the bridge pictured above. Besides separating off part of the arch into a thin, relatively unstable segment, this form of longitudinal cracking below the spandrel wall tends to reduce the amount of weight the bridge can handle. The spandrel wall actually plays a role in helping the arch support weight, and, if the spandrel wall is separated from the main part of the arch in this fashion, it can no longer strengthen the rest of the bridge.