Hi Banfa, a BASIC webpage page renders fine in every browser with or without the doctype, and to remove the doctype is just an easy solution for this.
Take a look at 1 of my sites:
http://www.imagine-x.net/index.php
There are still quite alot of sites out there that do not specify a doctype.
The standards say that a DOCTYPE should be included and generally speaking it is never a good idea to write non-standard code. It makes the code platform implementation dependent and can cause maintenance issues (when things that where never in the standard get dropped).
In fact the HTML standards where introduced because of the way MS and Netscape were diverging causing coding problems with you wanted you pages to appear correctly on both.
Learning to write your code in the correct standard is a good habit to pick up and like anything that needs learning it is easier to learn on the simple examples and then apply your knowledge when a more complex example comes along rather than just write your code any old way that seems to work in the simple examples and then having to learn the standard that you should have been using all along when you get the complex example that must be written to standards in order to work.
Working to standard breeds good reliable code that works cross platform, has lower maintenance, better accessibility and is more future proof.