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TL;DR: tons of support (and complications) at each level. One sequence can't fit all (it didn't claim to), but it makes sense in general, and so do the exceptions, and so do other motive models.

Check out Kenrick and colleagues' (2010) recent article. Kenrick is a prominent evolutionary psychologist; he and his colleagues have "renovated" Maslow's motive hierarchy based on a little bit of everything, including evolutionary, biological, personality, social, and cultural psychology. It's got some speculative theoretical claims of its own, but offers a deep review of empirical research too, and attempts to synthesize them. I'll just quote some of the parts that reference other research here (without vouching that all of it is necessarily original or empirical) to give you a sense of where else you might look beyond this article itself, and how Kenrick and colleagues summarize their basic findings directly. They go much further than direct summary though, so as other answers here have noted, there are many alternatives to Maslow's (1943) original theory, including this one!

An updated hierarchy of fundamental human motives...integrates ideas from life-history development with Maslow’s classic hierarchy...adds reproductive goals, in the order they are likely to first appear developmentally...[and] depicts the later developing goal systems as overlapping with, rather than completely replacing, earlier developing systems. Once a goal system has developed, its activation will be triggered whenever relevant environmental cues are salient. [Emphasis added.] The overlapping triangles...explicitly reflect...that later developmental needs and goals add to, rather than replace, existing ones... Summary of Developmental Level of Analysis Developmental...life-history theory suggest[s]...revisions to Maslow’s original hierarchy...Three later-developing reproduction-focused goals of mate acquisition, mate retention, and parental care...different motives in the hierarchy continue to operate alongside those that develop later in life...reflected visually by the overlapping triangles...Important individual differences in motivational priorities...result from interactions between development and current environment... Conclusion Developments [in] evolutionary biology, anthropology, and psychology...suggested...structural modifications to Maslow’s classic hierarchy of human motives...The ultimate functions of behaviors and of life-history development [suggest] explicit inclusion of motivational levels linked to mating and reproduction. Reproduction...is not ultimately about self-gratification, but involves a considerable diversion of resources away from selfish goals and toward other[s]...Life-history trade-offs also [imply] that later developing motive systems never fully replace earlier ones...they continue to coexist, ready to be activated depending on current opportunities and threats in the environment, in interaction with individual differences. Thus...the ongoing dynamic interaction between internal motives and their functional links to ongoing environmental threats and opportunities.

See also Table 1. How Different Motivational Systems Are Triggered by Proximate Cues and Individual Differences Linked to Fundamentally Important Threats and Opportunities.

Obvious critique: some healthy people don't want kids, a mate, or even sex. I bet Kenrick would call them rare expressions of individual variations that society maintains to round itself out in adaptive or reactive ways. I've also covered some other perspectives in this answer to a related question of social needs.

General themes from the rest of the article:

Support for existence of many underlying mechanisms associated with each level Some mechanisms are not definitionally tied to any one level.

Developmental, sociocultural, and individual differences in the order of emergence Maslow (1943) anticipated this, and presented his ordering as a general trend, not an inflexible, absolute sequence.



References

Kenrick, D. T., Griskevicius, V., Neuberg, S. L., & Schaller, M. (2010). Renovating the pyramid of needs contemporary extensions built upon ancient foundations. Perspectives on Psychological Science, 5(3), 292–314. Available online, URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3161123/. Retrieved January 30, 2014.

Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370–396. Available online, URL: http://downloads.joomlacode.org/trackeritem/5/8/7/58799/AbrahamH.Maslow-ATheoryOfHumanMotivation.pdf. Retrieved January 30, 2014.