The same rules that apply to the pill also apply to NuvaRing, the hormonal ring that prevents pregnancy. The situation is quite similar for women who have their Mirena IUD removed, as well. The hormonal IUD works in a way that can be compared to the pill, while also interfering with implantation through its presence in the womb. Many women report a few irregular menstrual cycles before everything settles into its normal rhythm again. Your ovulation is likely to be back within a few months after having your Mirena coil taken out. Depo Provera, the injectable form of hormonal birth control, is another popular method. While depo Provera is very effective and can prevent pregnancy for years at a time, it's a little trickier for women who do want to get pregnant.
Not only do you have to wait out the period of time the injection was supposed to work, many women who are trying to get pregnant after depo Provera say that their ovulation doesn't return for a long time after stopping the injections. Others get their fertility back soon, so don't despair, but do think about discussing your pregnancy chances with your OBGYN. Non-hormonal contraceptives like condoms and the copper coil (and... is there anything else, really?) are much easier to deal with. You can stop condoms and try for a baby right away, though you should of course make the same health and lifestyle chances anyone trying to get pregnant makes. The copper IUD needs removing, but your fertility will be back right away after it's gone.