Sorting cells by their type is an important capability in biological research and medical diagnostics. However, most cell sorting techniques rely on labels, which may have limited availability and specificity. Sorting different cell types by their different physical properties is an attractive alternative to labels because all cells intrinsically have these physical properties. But for some physical properties like cell size, the relatively large cell-to-cell variation within a cell type can make it difficult to identify and sort cells based on their size. In this work we sort different cells types by their density, a physical property with much lower cell-to-cell variation within a cell type (and therefore greater potential to discriminate different cell types) than other physical properties. We accomplish this using a 3D-printed microfluidic chip containing a flowing micron-scale density gradient. Earth's gravity makes each cell in the gradient quickly float or sink to the point where the cell's density matches the surrounding fluid's density, after which the cells are routed to different outlets and therefore sorted by their density. As a proof of concept, we use our density sorter chip to sort polymer microbeads by their material (polyethylene and polystyrene) and blood cells by their type (white blood cells and red blood cells). The simplicity, resolution, and throughput of this technique make it suitable for isolating even rare cell types in complex biological samples, in a wide variety of different research and clinical applications. We also demonstrated a technique for controlling microfluidic chips that requires no off-chip hardware. We accomplish this by using inert compounds to adjust the densities of fluids in the chip. When fluids of different densities flow together under laminar flow, the interface between the fluids quickly reorients to be orthogonal to Earth's gravitational force. If the channel containing the fluids then splits into two channels, the amount of each fluid flowing into each channel is precisely determined by the angle of the channels relative to gravity. This approach allows for sophisticated control of on-chip fluids with no off-chip control hardware, significantly reducing the cost of microfluidic instruments in point-of-care or resource-limited settings.