The widely known Hermann-grid illusion (Hermann 1870).
Dark patches appear in the street crossings, except the ones which you are directly looking at.
The classical explanation
1. Why do we see the dark patches?
Look at the diagram below and assume an on-center retinal ganglion cell. Its receptive field is indicated by the reddish disk. When the ganglion cell is, by chance, looking at the grating so that its centre ('+') is positioned at a crossing (top), there are 4 bright patches in the inhibitory surround. A ganglion cell looking at a street (bottom) however only gets 2 inhibitory patches, so it will have a higher spike rate then the one at the crossings.
2. Why don't we see the patches when we look right at them?
Because then we direct the fovea at the crossings, and in the fovea the receptive fields are much smaller... With such small receptive fields it obviously does not matter whether they are at the crossings or not.