Does ordering online negatively affect warranties for electronics such
as plasma TVs?

Buying online is not in and of itself an inherent source of problems
with warranties.  However, many online sellers of electronics engage
in business practices that can result in warranty service problems.

The phenomena creating the problem is known as "gray market" goods. 
In most cases, for a warranty to be honored, the product must have
been sold by an authorized reseller and must have been intended for
the market of the country where it is sold.

Some companies have discovered that they can import goods intended for
other country's markets at relatively low prices and then resell them
in high-priced markets like the United States.  These products may not
function correctly because they do not accept United States power
outlets, may not include English language manuals, and will in most
cases not be eligible for warranty service in the United States.  In
some cases, the products may be refurbished instead of being new.

The best way for you to protect yourself is to verify that the company
you are buying from is an authorized reseller for a manufacturer. 
Contacting the manufacturer to confirm that the company you will be
buying from is authorized to sell the product you are purchasing in
the market where you are purchasing it is a wise step to reduce the
chance of any problems.

Sincerely,

Wonko

Sources:

"Beware the Gray Market" HomeTech Solutions
http://www.hometech.com/home/graymarket.html

"Gray Market Products" by Shirley Rooker, Call For Action
http://www.callforaction.org/tips/detail.asp?id=22

"Camera Confidential" by Daniel Tynan and Tom Spring, PC World
(February 2003) http://www.pcworld.com/resource/article/0,aid,107855,00.asp