I presently have three websites. I have just created a new website that will combine all the services the three websites have. I want to have any traffic that comes to these established websites to be directed to the new website. Also, would like to discontinue the host service accounts for the three websites but maintain the domain accounts. Can this be done without being penalized by search engines?

You can use 301 redirects at your registrar - if it is an offered service. that is the search engine friendly way to do it that transfers the PR from your old sites to the new. Godaddy offers 301 redirects. Do not use 302 redirects or "masking".

So redirects can be used with maintaining the old websites?

What about aliasing?

From your original post I was assuming that you did not want to maintain the websites - just maintain the domains and redirect the traffic from them to a new website. Is that not correct? The 301 redirect method is the only way really to do that and receive any kind of benefit is search engines.

Aliasing, if I understand what you mean by that term, would equal duplicate content and not help. It would likely hurt your rankings rather than help.

I want to close down the websites, if possible.

If you have websites that are producing then don't even think about shutting them down. Develop the new site and let them all compete with each other. You already did most of the work, why ruin it.

The more sites you have the more opportunities you have to be found in by the search engines.

If they are stand alone sites you can host them all on the same account to save money. I have about a dozen sites on 1 account at godaddy.

creating an .htaccess file is also a good approach so that you won't lose any SEO efforts and ranking.

Use Google Webmaster Tools to update new site , so that you don't loose SEO efforts

Hi,
I think you have to go for 'canonical tag', this is the right solution to solve your problem.

Hi,
Go for 301 redirect, it will solve your problem definitely.

I would keep all three websites going. You can link them together, but if your websites are already live I would keep them up.