Y-DNA
R1b, which originated in western Europe, is the most common Y-DNA haplogroup among Irish men, at a frequency of about 81.5%. I1 is the second most common with 6%, followed by I2b at 5%, R1a at 2.5%, and E1b1b at 2%. G2a is found in only about 1%. Also rare are I2a (1%) and J2 (1%).
Mitochondrial DNA (mtDNA):
about 38.5% of Irish people carry mtDNA haplogroup H (of whom 11% are in H1 and H3), 13% carry U (of whom 2% are in U2, 0.5% are in U3, 2.5% are in U4, and 6% are in U5), 12% carry T, 11% carry K, and 10% carry J. Several others are encountered at smaller frequencies: 4% in HV0 and V, 3% in I, 2.5% in W, 1.5% in X2, and 4.5% in other(s).
Red hair
According to The ALlele FREquency Database, 8.4% of the 226 Irish people studied carry at least one T allele in the R151C (rs1805007) gene where TT always causes red hair. That isn't the only red hair allele that Irish people sometimes carry. Between 4-6% of 23andMe's Irish customers carry the T red hair allele on the R160W (rs1805008, Arg160Trp) gene, while 4-6% of their Irish customers carry the C red hair allele on the D294H (i3002507) gene.