How can I tell if my wheels need replacing due to rim wear? I have v-brakes which have started to groove my rims. What is the surest way to know if they need replacing?
Most rims have a little dimple or a groove (called wear indicators) for detecting rim wear. When this dimple or groove disappears, its time to get new rims. If the wheel physically damaged, take it to a LBS for an assessment on if it needs to be replaced or can be repaired anyway (e.g. cracks, dents, etc.). 

If your rim doesn't have wear indicators, take it to a bike shop, and they'll measure the rim widths with a caliper and check for deformations. I don't have a good threshold for what thickness would be considered acceptable, but I'd err on the side of caution. 

If your v-brake is grooving your rims, are you sure brake pads are still good? If you hit the metal back plate, they'll start destroying rims. If the groove is on the brake pads (due to the wear indicator or misalignment), you can sand it down if theres still enough material left, or just put on new pads.