Can I see videos through a cable connecting from my digi cam to my tv?

I want to purchase sony or cannon or nikon in about 5000 to 10000. I don't want to miss my family's precious moments. I want to see them in big screen specially videos. So please please suggest me a good camera i need it soon

You should not store and watch your videos from your camera.
Transfer it to your computer and then onto a DVD to be sure not to lose your family's precious moments.

Just about any camera on the market today will have this option. The cable needed may be an optional extra. Just look for a camera and once you found something nice look it up on the manufacturer's website.