Just wondering what can companies do when someone else's site is similar to their own?

This is just a suggested order:

1) Take a snapshot of the copying
2) Write a friendly email asking about the copying and explaining the situation and what you would request
3) If the response is good, you're done. If not, it would be time to decide whether its worth your time to have a lawyer write a formal letter.
4) Get a lawyer. Have them write a "legal" friendly letter.
5) The lawyer then knows best from here

But get a third partie to do this. - incase you are accused of altering screenshots.

Then people can claim you are co conspiring if its a friend of yours. :P

And I think you want the person to modify their site enough that it does not look like yours.

I am not so sure that a judge would accuse someone of altering the screenshots. The bottom line is that the site looks like yours. Is it practicle that someone is going to modify the screenshot to look like it even more? Simple screenshots of your site and screenshots of their site with some sort of time stamp of when the shot was taken, was fine.

I had this happen to me with my previous company. The nice email didn't work, but then the screenshots sent with the lawyers letter did.

You can request the site be taken down under the DMCA by contacting the infringer's ISP, informing them of the copyright infringement, and demanding the infringement to stop (take down material or site). As long as you can show the ISP reasonable proof of infringement, the ISP will likely take it down since they are satisfying their own Terms of Service. The ISP doesn't have to take it down, but if they don't, they risk being liable for the copyright infringement. It may piss of the infringer, but they can't turn around and sue the ISP (the DMCA protects the ISP).
:secret:

About 90% of the time, a simple cease and desist letter will get the copyright infringement taken care of. I have used a cease and desist letter many, many, times. The offenders have never ceased to comply yet.