Which is the best source to get the free website template, royalty free?
I know you have asked for royalty free, free templates and I have listed a few sites, but I have also listed some royalty free, paid template sites as well.
As already stated, free templates usually come with terms & conditions where you have to credit either the author or the site they came from in the form of a backlink with specific rules on the form of the link and anchor text.
The paid sites have catches as as well. Take for example Boxed Art. Their terms stipulate that you have to register your clients on their site and that you have to have a current membership to do this. This means that you can't download loads of templates during the 1 month membership then continue to develop templates for clients afterwards.
But Boxed Art does give access to a lot of sister sites with free stock photos, clipart (urgh), logos, branding, print templates etc.
Hope this helps.
Royalty Free (Free templates)
http://www.freewpthemes.net/ (Wordpress themes)
Royalty Free (Paid Templates)
http://www.templatemonster.com/ (per template pricing)
http://allwebco-templates.com/ (per template pricing)
http://www.designgalaxy.net (per template pricing)
http://www.boxedart.com/ (subscription basis)
http://www.pixelmill.com/Default.aspx (subscription basis)
I often use templates from http://www.freecsstemplates.org/ The good thing about these is that they all follow the same pattern and naming convention so it's real easy to switch between different designs. You can quickly try out several different designs before you decide.
They are completely free (and royalty-free) to use for any personal or commercial purpose provided you credit the freecsstemplates website in the form of a link back to the site.
Your question is rather broad so I will try to make it as simple as possible.
The best place for a website template largely depends on the kind of website you are aiming for and what framework you will be using. This should be your first step, especially as websites that offer themes an/or templates are often specialized in or focussed on a specific framework such as: Joomla (best for websites), Drupal, Wordpress (best for blogs), Magento (best for e-commerce / webshops) or self written (where you do all the coding yourself).
Website templates are becoming more and more sophisticated based on new framework developments and improvement of available technology. Please make sure that in case you are opting for a solution other than doing the coding yourself you would want to select one that is open-source and has a thriving community behind it.
When it comes to the templates I have summed up the major option above and I will give you some recommendations for each of them:
Drupal - Theme Shark
Magento - EM Themes
Please note: These are my personal recommendations and there are many others out there.
Obviously free themes are offered and for some purposes these are just fine. However, in most cases paying the $30,- to $80,- is money well spend. Quality XHTML / CSS, splendid designs, fast page loading, built in tools, widgets and plugins, support etc etc. So that would be a point that might be worth reconsidering...
For the rest. Enjoy!
By "royalty-free" do you mean "no cost at all" or do you mean "buy once, re-use often"? Royalty-free doesn't necessarily mean that you don't have to pay for it. It just means that you don't have to pay every time you use it. If you are looking for free (no cost) templates, I'll second www.freecsstemplates.org. It's good, but templates don't usually include source files, so it might be hard to modify templates.
If you want free (buy once, re-use often) templates, I'd recommend templatemonster.com or templatesbox.com. Those sites offer subscriptions so you can download and use as many templates as you want. Also, I'd look at themeforest.com. They have low-cost templates (typically $25-$50 USD) that you can use on multiple sites.
OpenSource Web Design http://www.oswd.org/ has 2000+ XHTML and CSS compliant files. Over 1700 of them are free and of high quality. If you have basic html and css knowledge they are easily customizable, and with a few hours work will rival custom designs.