Orange tree growth 
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The orange tree growth data, originally taken from Draper & Smith (1981) and reproduced in Draper & Smith (1998), p. 559, was used by Pinheiro & Bates (2000, Ch. 8.2) to illustrate how a logistic growth curve model with random effects can be implemented with the S-Plus function nlme. The data contain measurements of trunk circumferences (mm) made at seven occasions for each of five orange trees. The data is available within R in "datasets::Orange".

The errors within trees are assumed to be normally distributed and independent; the data can be straightforwardly analyzed either by standard nonlinear regression (assuming each tree follows an independent growth curve) or by nonlinear mixed-effects models (allowing the growth parameters to be random variables from an underlying population distribution).