A phenotype such as hair color like blonde hair. I am curious because mutations cause new alleles but does that mean that there always has to be a dominant or reccessive allele?
Can there be only one allele at a given locus?
An allele is a variant of a gene. If there is only one allele at a given gene, it means that there is no genetic variance at this specific locus (a locus is a position in the genome. It can typically correspond to a gene). It is not rare at all that the whole population is fixed for the same allele at a given locus.
Number of alleles
In courses, it is common to consider only the case of 2 alleles. In reality, there might be any number of strictly positive allele. At a given locus, you might have 1, 2, 3 or 11 alleles for examples. The reason why we typically teach about the 2 allele case is that 1 allele is not of much interest as there is not genetic variance at this specific locus and 3 or more alleles makes everything a little more complicated.
In courses, it is also common to consider diploid individuals, 2 alleles and the phenotypes of the three possible genotypes assuming $h_N = 1$ (see here to understand $h_N=1$). In reality, the relationship between two alleles may be vastly more complicated. There is a gradient from complete recessivity to complete dominance (passing through perfect additivity). It is also possible that the heterozygote is more extreme than any of the two homozygotes.
Dominance relationship - Number of alleles
As the number of alleles varies, any pair of alleles have a specific relationship of dominance. While empirical studies suggest that if allele
A is dominant over
B is dominant over
A is likely dominant over
C, it is not impossible that
C could be dominant over
A. And again here, I am considering only cases of complete dominance but any scenario is possible.
Dominance relationship - Ploidy
The ploidy also varies from one species to the other (and also from one moment in the life cycle to the other for sexually reproducing organisms). If you have a polyploid, then the number of possible genotypes is higher than 3 (even for a 2 allele case) and therefore the concepts of recessivity and dominance don't necessarily apply that easily.
Dominance relationship - Epistasis
Finally, there might have interaction between loci making that the relationship of dominance at one locus may depend upon the genetic background (that is the other variants present at other loci). Of course, it may as well depends upon the environment but let's not talk about that for the moment.
This is actually a really good question.
Can a phenotype only have one allele?
Yes. Some diseases arise only from one known allele. Some common phenotypes can be predominantly controlled by a single allele, but are affected by more than one. On an individual level, it is common to see one allele creating the phenotype, such as rare diseases cause by de novo mutations or familial rare disease. On a population level, it is harder but not impossible to find a phenotype that has only one allele for everyone because genes typically contain many alleles.
Mutations cause new alleles but does that mean that there always has to be a dominant or recessive allele?
No, there doesn't. In fact, we've lied to you in school a little bit to make things less complicated. It is easy to teach dominance and recessive alleles and do punnet squares, but the reality is that dominant alleles have little effect on complex traits like height or how much education someone receives. You've stumbled upon the same intuition that led Fisher to develop the currently prevailing additive model in 1918.
All complex traits, i.e., most things that aren't a rare or Mendelian disease, do not have important dominant/recessive alleles. Instead, each allele contributes a little bit regardless of if other alleles are present or not. So not only does there not have to be a dominant or recessive allele, but it is the norm for there not to be.
Dominant alleles arise naturally due to loss of function mutations. They are very important in the discussion of monogenic genetic diseases, and frequently contribute to the phenotypes of rare disease, even though they are rarer than additive alleles.
This may depend on how precisely you wish to define an allele. Cystic fibrosis is a disease effected by mutations in a chloride ion transport channel. Because this is an extensively studied illness, now over 500 different mutated versions of the gene are known. Each of these genotypes gives rise to the disease although there is much variation in the severity of the disease pending the exact mutation. https://www.ncbi.nlm.nih.gov/pubmed/8949420