In bibliometrics, only a few publications have focused on the citation histories of publications, where the citations for each citing year are assessed. In this study, therefore, annual categories of field- and time-normalized citation scores (based on the characteristic scores and scales method: 0 = poorly cited, 1 = fairly cited, 2 = remarkably cited, and 3 = outstandingly cited) are used to study the citation histories of papers. As our dataset, we used all articles published in 2000 and their annual citation scores until 2015. We generated annual sequences of citation scores (e.g., ) and compared the sequences of annual citation scores of six broader fields (natural sciences, engineering and technology, medical and health sciences, agricultural sciences, social sciences, and humanities). In agreement with previous studies, our results demonstrate that sequences with poorly cited (0) and fairly cited (1) elements dominate the publication set; sequences with remarkably cited (3) and outstandingly cited (4) periods are rare. The highest percentages of constantly poorly cited papers can be found in the social sciences; the lowest percentages are in the agricultural sciences and humanities. The largest group of papers with remarkably cited (3) and/or outstandingly cited (4) periods shows an increasing impact over the citing years with the following orders of sequences: (6.01%), which is followed by (1.62%). Only 0.11% of the papers (n = 909) are constantly on the outstandingly cited level.