I have been getting hit with people using my credit card -
fraudulently - after I have used the card on the internet.  How can I
prevent credit card theft?  (I often use WI FI in my suburban home?

Obviously, cancel all the cards that you've used on the Internet - if
you haven't done so already.

WIFI is notoriously insecure and you should also stop using cards
while you have this installed.

I will leave it to a real expert to advise you how you can better
protect yourself but I do know several folk who have stopped using
WIFI - for whatever reason.

Bryan

If you are connecting to a reputable store, you should be using SSL. 
Nothing is 100% safe, but if you are on SSL - your communication to
the vendor is encrypted as it passes over the wifi.  It would take a
very technically savy person to brute force decrypt your transmission.
 It would be much more likely that they get the informaton from
somewhere else...

You shouldn't necessarily drop WiFi altogether, but you should encrypt
your WiFi connection. If you don't, all the information you are
providing on it is open for anyone to intercept.

Credit cards can also give you temporary numbers that work for one
purchase each, but even logging into your credit card's website is not
safe on an unencrypted connection and your password could be sniffed.

Encrypt, encrypt, encrypt!

There's several things that you can do to cut down/minimize the problem.

First up, as other people have mentioned, encrypting either your
wireless connection and/or making sure that the connection to the
website is encrypted (SSL) is a good idea. To be honest though I'd be
real surprised if your wi-fi's the poblem.  If you think about it to
attack that you need to have someone within about 200ft of where you
are actively trying to grab your traffic.  Also as vballguy said most
sites use SSL and without some fairly tricky work it's pretty hard to
compromise SSL.

So here's some other things you can do.  

1. Anti-Spyware/A-V/Firewall.  Keep these on your machine and up to
date, one of the major ways that credit cards get stolen these days is
key stroke loggers and trojans delivered by malware.

2. Don't ever use Computers you don't know/trust to put in any
sensitive information, as there's a much higher chance of them being
infected with spyware etc.

3. Get a low-limit credit card to use on the Internet.  that way if
your card is compromised at least there's a limit to how much can be
taken (of course you should get your money back from the CC company
but that can take a while)

4.  A really good option if you're buying from sites that your not too
sure about is to use a "one-time" credit card.  these are cards where
you generate a new number for each transaction, one example of them is
here http://www.citibank.com/us/cards/tour/cb/shp_van.htm.

Rory

Odds are your card got nabbed from a database that was stolen.
A lot of online merchant web sites have the option to 'remember' your
card(s) so next time you shop with them, you can just select the card
you want to use from a list. Less ethical web site owners will partake
in this practise without telling you or allowing you the choice.
This is a huge mistake to make with your credit card information.
allowing a web site to store your credit card details is no different
than throwing a carbon from your credit car slip in the trash
un-shredded.

There are almost 30% more thefts of databases than what are actually
reported every year.(it gets a compnay into a liability situation if
they do report their data stolen, so they may not report it at all if
it happens, afterall, how can you prove that company A's database was
stolen unless you did the stealing?)

The safest bet would be to not use your credit card online, but in
today's world it is becoming lesss and less of an option.
Your next best bet would be to use a 'buffer' between your credit card
and the merchant, something like PayPal that would offer you some
layer of protection from fraudulent use along with the protection that
you get from your credit card.
One other method that you may want to use is use a specific card for
specific merchants or purchases.