Its worth noting now that for most websites manual search engine submission is unnecessary - at least for English websites.
For example almost 100% of all people search on google, bing, aol or yahoo. Yahoo is now run off bing, which means there's only really 3 search engines to worry about. If your website is receiving traffic then it should be indexed effectively by all three. You can help pages get ranked fast and help the engines crawl your website by manually submitting a site map.
As a general rule though, if a website and its pages are easily crawable and can be navigated then they will be indexed. This doesn't always mean that they will rank well however, which is where things like keyword optimisation and external linking come into play.
Mailbox Rental | Surrey Homecare