This is a question everyone is asking ...

The principle is the same but the operation is sometimes different depending on the engines!
So here are a few, but in a non-exhaustive list just waiting to be filled ...

Submit a website to Google

Submission is totally free, but it requires some time, quite variable depending on the period. You will also need a Google account :
https://www.google.com/webmasters/tools/submit-url

Submit a website to Bing

Idem, submission is free and you don't need to have a Bing account:
http://www.bing.com/toolbox/submit-site-url

You can choose to sumbit a website using the Bing Webmaster Tools. But you will need a Microsoft account:
http://www.bing.com/toolbox/webmaster

Submit a website to Yahoo

Since Yahoo! Search has merged Site Explorer into Bing Webmaster Tools there's no need to make the job twice anymore.

Submitting to Other Search Engines and Directories

Why stop at the giants. There are a lot of other search engines and directories on the Web which still can generate traffic to your site. The following list details how to submit to them:

Never use automated submission service for search !

When you use this kind of services, you don't really know exactly where the website will be submitted. This can be on more than 100,000 directory ! And search engines, like Google, really don't like everything which is not done in «a natural way» ...

So, use it at your own risk !