This is one of the most widely used Flash players on the Internet. It's free, stable and comes with plenty of support/documentation. The only downside is it's not really flashy (pun intended), but kind of plain and gets the job done.
Thanks Rictor! I'll check it out and play with it. If anyone else has any other suggestions in the interim please do share. I'm looking for something that would fit the aethetics of the site I mentioned in my first post.
I downloaded it and tried it on a test page. I liked the ease of use and the video plays nicely but the numbers that come up are a little blocky (this is probably what you meant by not flashy
I'd be willing to pay for a player (up to $200) if it looked better than the one I currently am using at http://psychicdeals.com but don't know where to look (my googling results in flash players that are for the end user who wants to view flash videos...but hasn't related to web designers who want to display flash video on their sites).
I also tried ivcsoft's player and it looked great but I couldn't get it to autoplay and there was no support available so I had to abandon that one.
Any other suggestions would be greatly appreciated!
edit: If it's any help, you can also change the colours on Jeroen's FLV player to match the website, which should give you a bit more customization to work with.