Is uniform noise present in some real processes?
Typically, when a real value $x$ from a sensor is discretized ($x_Q$) with a uniform quantizer, the error $x-x_Q$ is likely to be uniformly distributed.

Caveat: as commented by @bone, this can be stated in precise terms, see for instance:


A necessary and sufficient condition for quantization errors to be uniform and white,A. Sripad and D. Snyder, 1977



  In this paper, a necessary and sufficient condition is given to model
  the output of a quantizer as an infinite-precision input and an
  additive, uniform, white noise. The statistical properties of the
  quantization error are studied, and a detailed analysis for Gaussian
  distributed inputs is given.



Statistical Theory of Quantization, Bernard Widrow, Istvan Kollar,  Ming-Chang Liu, 1996



  The effect of uniform quantization can often be modeled by an additive
  noise that is uniformly distributed, uncorrelated with the input
  signal, and has a white spectrum. This paper surveys the theory behind
  this model, and discusses the conditions of its validity. The
  application of the model to floating-point quantization is
  demonstrated.