The membrane folds of dendritic cells
Yes, these include:


neurons
melanocytes
Merkel cells


In all cases, as you suggested, their function is to extend the surface area of the parent cell. In the case of neurons, the role of dendrites, which receive the vast majority of synapses, is to maximise the number of synapses the cell receives from different pre-synaptic partners (Chklovskii et al. 2002, Chklovksii 2004). In melanocytes, they are used to transfer melanin to keratinocytes. In Merkel cells, they are again used in order to form synapse-like connections with neurons (Mihara et al. 1979).

The word originates from the Greek δένδρον, which means 'tree'. Dendritic structures are found throughout in nature, including in...trees, where presumably they are used to maximise exposure to sunlight. Theoretical studies on the formation of dendritic arborisations in neurons indicate that they are governed by at least these factors: i) repulsion between dendrites (Wen et al. 2009), ii) minimisation of dendritic volume used (Tamori 1993), possibly through resource competition (Graham and van Ooyen 2004). It is an intuitively attractive idea to think that similar processes govern dendrite-like formation in the other biological systems described above as well.  




References
- Chklovskii, D. B., Schikorski, T., &amp; Stevens, C. F. (2002). Wiring Optimization in Cortical Circuits. Neuron, 34(3), 341–347. https://doi.org/10.1016/S0896-6273(02)00679-7
- Chklovskii, D. B. (2004). Synaptic Connectivity and Neuronal Morphology: Two Sides of the Same Coin, Neuron, 43(5), 609-617. https://doi.org/10.1016/j.neuron.2004.08.012
- Graham, B. P., &amp; van Ooyen, A. (2004). Transport limited effects in a model of dendritic branching. Journal of Theoretical Biology, 230(3), 421–432. https://doi.org/10.1016/j.jtbi.2004.06.007
- Mihara M., Hashimoto K., Ueda K., Kumakiri M. (1979). The Specialized Junctions between Merkel Cell and Neurite: An Electron Microscopic Study, Journal of Investigative Dermatology, 73(5), 325-334. https://doi.org/10.1111/1523-1747.ep12550322.
- Tamori, Y. (1993). Theory of dendritic morphology. Physical Review E, 48(4), 3124–3129. https://doi.org/10.1103/PhysRevE.48.3124
- Wen, Q., Stepanyants, A., Elston, G. N., Grosberg, A. Y., &amp; Chklovskii, D. B. (2009). Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. Proceedings of the National Academy of Sciences, 106(30), 12536–12541. https://doi.org/10.1073/pnas.0901530106