If we charge a capacitor can we discharge it into a battery? I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.
 A: Crazy Buddy's answer and related comments have made the point that you could indeed use a capacitor to charge a battery, but the amount of energy stored in capacitors is generally less than in batteries so it wouldn't charge the battery very much.
However there is a new generation of capacitors called ultracapacitors that are being developed with electric cars in mind. See for example this blog or Google to find many such articles on ultracapacitors. It seems likely that if the technology ever makes it into electric cars it will be as a combination of a battery and an ultracapacitor. Since most cars use regenerative braking, the energy generated by the braking would be stored in the ultracapacitor and would then recharge the battery. So this would be an example of using a capacitor to charge a battery.
A: Let's take your question in my thought...
For instance, let us assume that we've got a capacitor of capacitance about some $100 \mu F$ and  Also, a commonly used $\text{Ni-mH}$ battery of some voltage $1.5 \text V$ with charge capacities about $2000 \text{mA-h}$
Energy of the battery would be $E=1.5\times 2000\times10^{-3}\times3600$ $$=1.08\times10^4 J$$
I really bet ya that a common capacitor of some micro-farads won't charge upto that energy.
A: A single Maxwell (for instance) BCAP0350 2.7v ultra capacitor that's about the size of a D cell has a capacity of 1300 Joules (1.3 x 10^3 J).  
It is extremely useful to use ultracaps to charge batteries if the nature of the power source is intermittent and high current (say, at 35 to 175 Amps, also within spec of the one I listed).
Charge the ultracaps fast with high current and subsequently use the ultracaps to slowly charge the battery without having to worry about the battery exploding or its life being shortened by high charging rates.  
Ultracaps have cycle lives in the millions, not the tens or hundreds like various battery technologies.
A: All you need to charge a battery from a capacitor is to have more voltage charged on the capacitor than the voltage of the battery. The size will only affect how much time the capacitor will charge the battery. If you could charge the capacitor over and over and discharge it into the battery every time it was full it would eventually fully charge the battery.
A: James Tipton is correct.  You don't need ultra caps or super caps.  Regular standard electrolytically will do just fine.  The key is to charge the cap higher than the battery and then discharge the cap into the battery   This must be done continuously and there must be no load on the battery.  Batteries have this nasty habit of not allowing its voltage to change just like coils don't allow current change. The process could take many hours or even days. But eventually the battery will charge full.  The circuit for the question of capacitors charging batteries has been made by me and posted on line.  See the videos page at www.silectronics.com.    Thank you
