Stubborn rings around the tub. An ordinary old school eraser is a useful item to keep on the edge of the bath. It will remove even the most stubborn of greasy rings.
General bathroom cleaning. A clever idea is to take a regular sponge and squeeze it down into the foot of a stocking or leg of a pantyhose. Tie it with a knot and that extra bit of gentle abrasion will do the job quicker when you are wiping down baths, basins and tiles, etc.
Scum removal. Need anyone be reminded that common old baking soda made into a paste with water is also a very effective way to clean anywhere?
Mould and mildew. To stop this mucky stuff from gaining a foothold in your bathroom, make your own spray. Take one cup of 3% hydrogen peroxide and add to one cup water. Put in a spray bottle and nag your family to spray this around the shower, bath, tiles and basin and then wipe.
This will save you a load of time and money, in the long run.