Reliable enough to use, and the figures are published rather than claimed. On this site the thirty facets of the 120-item Big Five test have coefficient alphas between .63 and .88 from a sample of 619,150 people, the five scales of the 50-item markers have alphas between .79 and .87, and Big Five scores hold their rank among a person’s peers over years, more so the older the person is.
Two kinds of reliability
Internal consistency, reported as coefficient alpha, asks whether the items of a scale hang together: whether someone who agrees with one item tends to agree with the others. Test-retest reliability asks whether the score holds when the same person answers again weeks or months later. Both run from 0 to 1, and for personality scales figures above .7 are generally taken as sound. Shorter scales score lower on alpha by construction, which is why a four-item facet and a twenty-four-item domain are not held to the same standard.
The figures on this site
The 120-item test is Johnson’s (2014) IPIP-NEO-120. The IPIP key page reports alpha for each of its thirty facets from an internet sample of 619,150 people: the lowest is .63 for liberalism, the highest .88 for cautiousness, and the extraversion facets run from .69 to .85. The percentiles compare you with 410,376 of those people, the rows left after anyone with a missing answer was removed. The 50-item test uses Goldberg’s (1992) markers, whose five ten-item scales have alphas from .79 for conscientiousness to .87 for extraversion on the key page, and its percentiles come from 603,322 people in a separate public dataset. The ten-item quick test has alphas as low as .40, as its authors expected of two-item scales; Gosling, Rentfrow and Swann (2003) report six-week test-retest reliabilities of .62 to .77 for it instead. Over longer spans, Roberts and DelVecchio (2000) reviewed longitudinal studies and found that the rank-order consistency of traits rises with age, from about .3 in childhood to about .5 in the student years and .7 or above after fifty, over intervals averaging several years.
What reliability does not mean
A reliable scale is not thereby an accurate one. Alpha says the items agree with each other; it does not say they measure what they claim, and a scale can measure a person’s self-image very consistently. An alpha of .63 on a four-item facet does not mean the facet is broken; it means that facet score will move more between attempts than the domain score, and should be read more loosely. Consistency over years is about rank, not level: a whole age group can drift while each person keeps their place in it.
What it means for your results
Trust the domain percentile more than any single facet, and a facet more than any single item. A change of a few points between two attempts is noise on every scale here; a change of a band, from the 30th percentile to the 60th, is more than the reliability figures would produce by chance. The methodology page lists every published figure for every test on the site.
The Big Five test takes about twelve minutes and reports the reliability of each scale on the results page, next to the sample it compares you with.