All of the most successful models for forming large scale structure assume that most of the universe is composed of cold dark matter.
Models in which the primordial fluctuations are adiabatic and the universe is comprised only of baryons and photons are ruled out by CBR observations. The predicted level of fluctuations in these models exceed the observed level by more than an order of magnitude. Isocurvature models  fare better; however, these models also appear to be in conflict with CBR observations .
The current ``best fit'' models have , , and either a cosmological constant or space curvature (see Steinhardt's talk in these proceedings for a review). These models fit COBE observations; are consistent with age and determinations; are consistent with LSS power spectrum, and are consistent with most large scale velocity measurements. While they are in conflict with the large velocities detected by Lauer & Postman , these large velocities are controversial . Numerical simulations suggest that these models also agree with the properties of rich clusters .
Despite the success of structure formation models that assume non-baryonic dark matter, no one has proven a ``no-go'' theorem that rules out baryon-only models. It is an interesting challenge to determine what observations are needed to rule out these models.