There are really 3 major things that can occur by not treating your varicose veins:

1. Nothing happens – If they are protruding outside your legs, they may look unsightly and just slowly get a little worse with no symptoms at all
2. If they were small initially, they may become larger and symptoms can worsen, like itchiness, swelling, heaviness, bleeding or wound formation. 
3. Small clots can form in the varicose veins and potentially lead to a clot in the deep system.

The challenge is not knowing which of the 3 you will be. Varicose veins is generally a slowly progressive condition but there are many whereby it progresses faster than others. It is sometimes very difficult to know.