In which contexts this situation appeared? How did you handle it? Also, if you used models that had more parameters than data points, how did you handle the situation?
Depending on the situation, it might not be an issue. For instance, in density estimation with adaptive kernels, each window might have its own radius, resulting in as many parameters (radii) as data points. In a regression problem, you run the risk of over-fitting though, unless you use ridge regression, dimension reduction, stepwise regression or other techniques.
So, how did you cope with this problem?