I am assisting an associate who is creating an online business selling
widgets (play along please!).  She has purchased ~12 domain names. 
One site will act as the "corporate" storefront and provide widget
reviews, specifications, support and other value added services.  Each
other site will focus on specific *applications* of widgets including
testimonials, examples, how-tos and case studies.

The sites would be something like this:

+ widgetsinc.com - *product* centric; registered business.
+ widgetsathome.com - *application* centric illustrating how widgets
are best used in homes using products available from widgetsinc.com
+ widgetsatwork.com - *application* centric focusing how to best use
widgets in offices and businesses using products available from
widgetsinc.com.
+ widgetsat_____.com - *application* centric using products available
from widgetsinc.com

A single machine has been purchased to host the sites and she
currently has *one* IP address for this purpose.  I have read in
numerous resources that hosting multiple, related websites can have
negative organic search results.  I have also read that sites that
resemble link farms are penalized by search engines.

My questions are as follows:

1)  Is there any negative impact in hosting all websites on the same
IP address?  The registrant information per domain is identical.
2)  Is there any risk in creating *relevant* links between the various
sites?  For example, a visitor might land at widgetsatwork.com and
come across an link that mentions how widgets were effectively used
for construction sites or a link that leads to a product review.
3)  #2 said another way, how can I be sure that Google (or other SE's)
would not negatively penalize the sites if they are hosted on the same
IP address (box) and link to each other?

I need to ensure that her planned setup does not get any of those
sites mistaken as SEO voodoo. We have nothing to hide and feel that
linking the sites as needed would ultimately benefit the end user.

Marc

You are answering your own question.
If your gut tells you not to use 1 ip then do not. 

This company http://www.keithcash.com helped me with the SEO for my
website http://www.poker-card-games-online.com

Yes, it does have a negative impact on your rankings. You might as
well save yourself the money and have all of the info in
subdirectories on one website. Paying for hosting and registration of
several domains is a bad idea.

You should do something like this:

www.widgits.com (main page)
www.widgits.com/specificwidget1 (subdirectory, remember you can also
have a different theme for this too)
www.widgits.com/specificwidget2 (you get the point...)

Rather than doing so much work on many sites like that, you should
just do a good reciprocal link campaign.

It shouldn't be as big a problem as you're saying. Since many sites
use VirtualHosting (multiple domains on one IP address), it's not such
a big deal. YRMV.

>1)  Is there any negative impact in hosting all websites on the same
>IP address?  The registrant information per domain is identical.


Yes. This will get flagged at some point, on some engines.


>2)  Is there any risk in creating *relevant* links between the various
>sites?  For example, a visitor might land at widgetsatwork.com and
>come across an link that mentions how widgets were effectively used
>for construction sites or a link that leads to a product review.


The intent is often taken into account in whether a site is penalized when 
it gets to a human, but automated systems will most likely not take this 
into account. If all the sites are on the same IP, they'll likely be penalized.
They'll even likely be penalized if they are on the same *subnet*, not 
even just the same IP. 


>3)  #2 said another way, how can I be sure that Google (or other SE's)
>would not negatively penalize the sites if they are hosted on the same
>IP address (box) and link to each other?


You can't be sure. You also can't be sure that they won't change their 
policy/algorithm/checks/penalties next week or next year.

Rather than setting up 12 different sites, it would be better to develop 
content that other sites will *want* to link to, relevant to your client's 
product and it's use.