I am involved in a project where I am likely to have a number of
client computers (say, 50) in one location that will all be running
the same client software that connects to a server.  Think 50
computers side by side playing spades on yahoo.
The thing is, I don't want it to be easily discernable by the company
I'm connecting to (yahoo, in this example) that all of my computers
are sitting in the same room.  Yes, I promise what I'm going to be
doing is entirely legal.
Again, I'm not talking about simple web services... if there's a web
proxy or anonymizer that does what I'm asking, I'm not aware of it,
which is why I'm asking this question.  I want the IP addresses of the
computers to look as dissimilar as possible.  If they all have the
same first three groupings in their IP addresses and the last is the
only one that varies, that is most decidely not 'covert'.  I would
take having the first two groupings the same as a last resort, but
would prefer more randomness.
Note:  if the IP addresses assigned are all very different-looking,
but all EASILY tracable back to the same service, this doesn't really
help.
What are my options?  I would prefer an option in the Seattle, WA or
Vancouver, BC area, if location matters for any of the options.

For the life of me I can not think of a single reason you would need
this either not illegal or not some kind of fraud.

I'm sorry you can't think of an example.  I am not going to say what
this is for, but for the record I have no problem with the accounts
being linkable by law enforcement or even a thorough investigation, I
just don't want a quick check to reveal the proximity in location.  I
would think that internet scammers have more anonymous ways to do
things that don't involve a clear paper trail of paying for services?

You can do that by having multiple IP's pools. You can use a VPN
server running in Linux (pptpd for example). In the configuration of
this daemon, you write a simple txt file with the various IP's from
the various pools in an random order. The ppptp daemon will assign the
IP's in a seemingly random way. Your users must use an VPN client to
conect to VPN server. The trick here is to use the VPN as a way to
assign IP's. DHCP would do the trick too.

The problem remains to obtain those IP pools. Maybe you can buy
various ranges from different ISP's. This probably will cost more than
if you had a single, continuous IP pool from a single ISP.

Hope this hint will help you.

This is not what I'm looking for.  The technical method of assigning
the IPs is simple.  It's acquiring the rights to the varied IP
addresses that is the issue.  In your scenario I would purchase IP
blocks from diff't ISPs.  This is cumbersome, and the 4 blocks would
each be connectable to each other.  In addition, managing the
ingoing/outgoing traffic would be cumbersome... might as well skip the
VPN and just have 4 networks.  I'm looking for a single provider who
will give me rights to many varied IPs.

It seems like it would be fairly easy to find 50 seperate proxies to
use for each computer. It would be very difficult for someone to find
who each request came from, especially if you use proxies that are
outside of the US.

Also, you could try something like tor (tor.eff.org) for some of your computers.

em... I think your requirements are somehow contradictory... If there
really exists a service provider that is able to assign 50 "quite
unsimilar" IP addresses to you, then those addresses would be easily
traced by services like whois, or it will simply help you get blocks
of addresses from ISP in different countries, then as what you have
said, it would be cumbersome to manage the traffics for the service
provider. You are not looking for web proxy either. So, I guess there
is probably no solution for your question.

As others have commented, the simple answer is there is
NO simple solution. The IP packets need to traverse
the ISP network. So your computer cannot put random addresses.
So either you need to get the 50 random addresses from one ISP
or from a collection of ISPs. Again as you've stated this is
cumbersome. Once you've obtained a set of 50 random addresses, 
you can do further randomness with tricks like NAT. You can
set up a simple NAT router to randomly assign addresses from this
50 address pool to various connections.

Another approach is (in a very simplisitic way) to have a proxy
for each computer in the room in someother geographically different
location (hence differnet ISP, different IP). A computer sends its
request to its proxy to relay the request to the server. This is
really expensive but a sure way to ensure the server cannot figure out
all requests come from the same place.

Note that every the very forwarding by routers use aggregated dest-ip
prefixes. So the request you are making is going against this way of
IP packet forwarding

im not sure if this is what you're looking for, but here is a program
that lets you have multiple adresses on a LAN.

here's the description:

Honeyd is a small daemon that creates virtual hosts on a network. The
hosts can be configured to run arbitrary services, and their TCP
personality can be adapted so that they appear to be running certain
versions of operating systems. Honeyd enables a single host to claim
multiple addresses on a LAN for network simulation. It is possible to
ping the virtual machines, or to traceroute them. Any type of service
on the virtual machine can be simulated according to a simple
configuration file. It is also possible to proxy services to another
machine rather than simulating them.

hope this works

mhylton, I do not believe that product would work for connections that
end outside the local LAN, but thanks.

karthikg, your answer has been the best so far i'd say, though not
really a complete answer obviously.  I am aware that the nature of IP
addressing and internet routing is such that dissimilar IP addresses
must go through dissimilar routing...

I appreciate the thoughts.  Sounds like I'd need to go the multiple
ISP route and get 5-10 IPs per, and hope that is sufficient.