Biological complexity is rather hard to define. You can count the number of levels of hierarchical organization (colony > individual > organ > cell > organelle > molecule), or the number of subcomponent, or their level of interdepedence. There have certainly been events where the complexity of organisms increased by all standards: the association of prokaryotes to form complex eukaryotic cells, the origin of multicellular plants and animals, the evolution of clonal (e.g. corals), social (e.g. humans), and eusocial (e.g. ants) colonies. They are pretty evenly scattered over the historyof life, and the various evolutions of sociality are fairly recent (eusocial insects are younger than dinosaurs).
SzathmĂĄry 2015 is a pretty good treatise of this sort of major complexity bumps. I also summarized the basic mechanisms here. McShea 2016 notices three parallel trends over time: sometimes, a new level of organization is added at the top (e.g. cells combine to form multicellular bodies); diversity increases one level down (e.g. differentiation of cells in more complex multicellular organisms); and diversity reduces two levels down (individual cells within multicellular bodies have fewer subparts than independent unicellular organisms, since they don't have to survive on their own).
McShea 2016, the "evolutionary syndrome". Left could be a unicellular alga like Chlamydmonas, middle a simple colonial alga like Volvox, and right a complex plant with specialized cell types.
AIUI even Stephen Jay Gould, famous for arguing that evolution has no large-scale tendencies and is largely driven by contingency, acknowledged that the complexity of the most complex organism at any given time increased since he origin of life, if for no other reason that increasing is all it can do when you start from a maximally simple organism. Others could say that there are sensible evolutionary reasons for complexity to increase. Certainly the idea that there is a universal innate pro-complexity tendency (technical term is orthogenesis) in all organisms is discredited for a good reason.
Nevertheless, many lineages become simpler. Yeasts are fungi that returned to unicellularity, and many parasitic animals lost most of their internal structures (shout out to Orthonectida, which reverted to having only two kinds of cells). Complexity certainly isn't the same as fitness or evolutionary success. After all, the most numerous known species on Earth is a marine bacterium, Pelagibacter ubique, with as many as a billion billion billion individuals, and the most common autotroph is another bacterium, Prochlorococcus.
Complexification is useful in many cases, to take advantage of scale economy and comparative advantage, but so is simplification. Depends on circumstances. There certainly have been many instances throughout the history of life in which the maximum complexity available to organisms increased, even though not all lineages necessarily became more complex.
Levin &al 2017, complexity transitions in imaginary aliens
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