Well it pretty much depends on the niche and mainly number of pages and content quantity of your site. If it is a small site guess there won't be need of such. If it has tens of thousand pages, then it might be a good idea. You have to decide depending on your site theme, navigation and particular content & products. Btw guess this should be put in some design or marketing forum sections, as I doubt it you will create a search engine for the entire planet, it will be limited to your own site, right?!
It depends on your site's category. If you are dealing with a b2b trade business, classified ads, article directory or similar sites with huge pages, you are going to need an internal search engine for facilitating your visitors. Otherwise, if your site is static with a little number of pages, it's not important but having a search engine may add value to your website interface and appearance. Enjoy
I feel that a search form is great if you have a blog type site with lots of details and posts. It'll keep visitors there longer.
Agreed with rmeeuwsen, if its a blog kind of site or really huge site then it will be worth to have site search.
It depends on you site need, if you put search engine in it, it will make visitors to search something via your search engine.
It depends upon your site data (no. of webpages), if it has less number of webpage than it is not too necessary, if large than essential.
Hello, I think website should not be depends to looks it should be informative. because for SEO, content is helpful for website.
I would say it is...if a users has an easier time finding a thing they are looking for on your webpage, they will stay more and recommend the service to friends.