Let's just take plastic water bottles for a start - have you ever left one in the sun or in a hot car and then tasted the water in it? It tastes of chemicals and not very nice... that's the chemicals leaching out of the plastic due to the temperature. Such chemicals (such as BPA) can be xeno-oestrogens - they mimic the oestrogen hormone in our bodies and as such, they disrupt normal body functions, which is not a good thing! Other chemicals in plastics are potentially carcinogenic - cancer causing.
Xeno-oestrogens can affect us in different ways - causing young girls to reach puberty from 7 years of age, causing weight gain, man boobs and shrunken genitals in men, and hormone/mood swings, breast cancer and disrupting menstrual cycles in women.
Allegedly BPA-free plastics are supposed to be safe, yet they are still made from chemicals that leach into your water/foods when heated. As a result, I recommend avoiding ALL plastic bottles and containers, and using glass or stainless steel (not aluminium) bottles or containers instead.
Some things you may not know:
1) Cooking foods in plastic (from ready-meals) or microwaving leftovers in plastic is about the worst thing you can do. The extreme heat generated by microwaves leaches much more of the plastic chemicals into your food.
2) Freezing foods in plastic has a similar effect to heating - as the plastic shrinks, chemicals are again leached into your food.
Anything that disrupts your hormones is very bad news for your health, as hormones control most of your body functions and are released in specific amounts for their required purposes. Any external sources of hormones such as from plastics is going to cause an unknown number of health issues.
Simple little things like not using plastic storage containers for food, and certainly not using plastic bottles for water or heating/freezing food in plastic containers can be beneficial to your health.
Good health to you!