Depending on what your rendering, Tiles can only save you a bit of memory.
While rendering, the GPU has to store the geometry, textures, render buffers/output and some code as well (might be more, not a expert really)
For rendering with Cycles, ALL of the geometry and ALL of the textures have to be stored in your GPU’s memory for the whole render.
Not having tiles means the whole output of the frame your rendering (passes etc…) has to be stored in the GPU which could be a 19201080 image, and with 5 passes that can take up a decent bit of memory, while if your using 256256 tiles, only each tile has to be stored.
If you have 600mb of textures, 1.1GB of geometry, and all passes used for 300Mb (no tiles) = 2GB used, but you OS might use a bit extra as well. This situation would Out Of Memory error if rendered with a 2GB GPU. Using tiles could reduce the buffer memory used to 30mb (hypothetically) thus using 1.73GB, and not crashing.
However, tiles won’t help all OOM errors if your rendering a huge scene, that is over your GPU’s memory by far.