Yes, the sitemap is a must for every site to make the Search Engine bots to get index all the pages. Indirectly it cuts the cost of indepth optimization of each and every page on the site.
For a fast and easy inclusion in the Google SERP you should ALWAYS use a sitemap and submit this to Google Webmaster Tools. You won't die if you do not use a sitemap but you won't make money either ;-)
In order to let spidy crawl your internal links you have to create a sitemap. It was like you have a restaurant and you have many branches but people doesn't know where is your other branches. So yes we really need sitemap for our website to let spider be aware of our website's internal pages.
I mean, when the google bots crawl my website don't they follow all links meaning they will index all my pages?
Yes. Sitemap is really necessary. The search engines while crawling through your site, found all the informations of your site only through sitemap. It reduces the time taken for the search engines to crawl through all your pages. So its necessary for you to have a sitemap for your website. To help you more with this, there are many sitemap generators available. I have used Sitemap Generator to generate sitemap.
well what is the best format for a sitemap? I have one of my sitemaps set up like this: <url> <loc>http://www.vietnamveteranscardonation.org/</loc> </url> <url> is this the best way to setup sitemaps?
Yes that is fine. It is the same structure I use. There are some more optional components, but none required.
I really sees sitemap as a tool that can help us get indexed by google and other search engines, that's all. No more and no less.
I read an article saying that sitemap is really useful for a big website, let's say it has 100 pages. I have a web around 10 pages, is a sitemap really necessary for this kind of small website too?
I think it is working on all kind of sites. No matter you got a big site with lots of pages, the sitemap still works even if you are just started.