What kind of data do you have? A 1-D signal? A 2-D grayscale or color image?
You can look at simple filters like median, average, Gaussian blur, or there are better but more complicated filters like BM3D, K-SVD, non-local means, Kuwahara (demo attached), K-LLD, etc. Last I checked BM3D was considered state of the art for images, and what everyone else tried to beat (usually unsuccessfully). There are non-local means submissions in the File Exchange.