Learn/Get-Your-Website-Indexed

How to check which pages on your website are indexed:

Try searching in Google for "site:yourwebsite.com" and see what turns up. This isn't 100% accurate, but it can give you a rough idea of what you're working with. This will tell you which pages are in the index, and usually if it's a little off it will show less pages than are actually in the index.
If you've submitted an XML sitemap via Google Webmaster Tools you can find the most accurate number of pages in your sitemap that Google has indexed. This will tell you the number of pages in Google's index out of the total number of pages in your sitemap, but it won't tell you which pages are indexed.
Use this tool...

Have a website with unique, valuable content that you would find valuable enough to serve in search results if you were a search engine. This is hopefully obvious, but a website without quality content is unlikely to get indexed no matter how hard it tries the other tactics below.
Creating an HTML sitemap can help search engines crawlers find and index more pages on your site, once they've found your website and "sitemap" link.
Get inbound links to your site. The primary way that search engines find new sites and web pages to add to its index and search results is by following links from other websites. Links without a NoFollow attribute (often called DoFollow links) are best, but NoFollow links may still be helpful (particularly if they're from a popular social site like Twitter).
- Ask a friend or related website to link to your site, get a DoFollow link from AboutUs.org, add yourself to some directories, etc.
If your site is brand new and doesn't have any pages in search engines yet, submitting it to search engines can help. Here is Google's submission form.
Let people know about your site...

If none of your website's pages are showing up in search engines, make sure you aren't accidentally telling them not to.

Look at the page source (in most web browsers, clicking ctrl and the letter U will do this) for one of your web pages and make sure that there isn't something like in there. If a "NOINDEX" tag is there, you will need to remove it because that tells search engines to go away and not put that page in its index.
Look at yourwebsite.com/robots.txt and make sure you aren't telling search engine spiders to stay out and not index a certain type of page with something like this: User-Agent: * Disallow: /Special/ (This as an example, tells all search engines not to index pages on AboutUs.org that have a URL like AboutUs.org/Special/something.)
Crawl errors in Google Webmaster Tools?
There's no good way to know for sure if Google or another search engine has penalized or banned your site, but... If an established website -- one that's been around for a while and has some decent inbound links -- has noticed a drop in traffic from that search engine and/or doesn't have pages indexed in search engines (like a Google search for "site:example.com" turns up nothing), a search engine penalty may be possible. Check Google's quality guidelines for a list of things to avoid and that they may penalize sites for.