Just insert the iframe code (in the html editor) and you are all set. No plugin needed.

Or if you really want a plugin, try Youtube Shortcode. (There are actually a few good ones, just search 'youtube' inside the 'add new plugin' search field.)

Might I ask, why don't you just want to embed the code from YouTube instead of using a plugin for this operation?

I have done this many times and it is simple. From Youtube take the embed code. Than on your site go to the HTML function of the page or post you want to have a video on and past it there, press publish and it is done.
Another thing I usually do is make it autoplay so it starts right away when someone goes to the site. For this I add ?rel=08amp;autoplay=1 to the embed code. This goes right after the Youtube video number and before the quote mark, this is usually about two thirds of the way thru the embed code. I hope this helps.

The embed code will get stripped. In newer versions of WordPress, you can just paste the YouTube URL on its own line and WP should generate an embed for you.

If that isn't satisfactory, this plugin (WordPress › Viper's Video Quicktags « WordPress Plugins) adds nice embed buttons to your editor in WP for YouTube and other video sites.

is this legal to put youtube in our website

Yes it is legal to put youtube videos on your site. Infact they want you to do so, that is why they have the share feature with every video. Occainsionally a video poster will set up their video so it can not be shared but this is rare.
I am not sure what strangerstudios means above when he says that the embed code will get "stripped". I did this as recently as yesterday with the most recent version of WP and it works fine. Of course he is correct that you can use the URL also.

Very strange. I still have to agree with using the YouTube shortcode under the "HTML" tab. Too many plugins can sometimes slow down Wordpress.

I have been told by my hosting company that too many plugins can be a bit of a problem so I try not to use too many, although this can be tough as there are some very good ones and I want to be thorough. It is a good idea to delete any you are not using and also to keep your plugins updated.