Dads eyes are blue. Moms eyes are brown. What color eyes is their baby likely to have?
Could be either but brown is more likely because brown is the genetically dominant colour.
Inheritance of eye color isn't that simple because it is polygenic. Polygenic means that the trait is influenced not by one gene, but by multiple genes working together. Even if only the one most obvious gene is considered--the one with the most control over brown vs. all other eye colors, there are still a few things to consider.
The parents' eye colors
Whether the parents are homozygous or heterozygous for that color
If the eye colors of the parents are dominant or recessive.
Each person carries two copies of every gene, one copy inherited from mom and one inherited from dad. Homozygous means that the two copies match (for example, maybe both copies are for brown eyes). If someone is heterozygous, it means that the two copies of the gene differ (for example, one for brown and one for non-brown). It's usually impossible to determine by looking at a person's eye color whether she is heterozygous or homozygous.
Dominance of one copy of the gene over the other means that the dominant copy has an effect you can see, in this case you can see that the person has brown eyes, and the effect of the other gene copy is hidden. Brown and maybe green are considered dominant. Thus a brown-eyed person may carry both a brown version and a non-brown version of the gene, and either copy may be passed to his children.