A small aliphatic ether, like diethyl ether, is slightly soluble in water. It has limited solubility, but as you said, is slightly polar. As you get larger aliphatic ethers, the solubility quickly drops off.
A cyclic ether like THF is fully miscible in water. This is a special case for ethers as the ring form "exposes" the lone pairs on the oxygen to a greater extent, allowing it to freely accept hydrogen bonds in water.