What is the best (defined below) web conferencing software for 3+ people at a time?

I quite like dozeo for all benefits you're looking for... They are easy to use, have a nice user interface, you don't need to download and install software. It's browser-based and participants can enter by just clicking on a link you provide. Check out: http://www.dozeo.com.

I am at the Head of Product at http://zoom.us. We provide a free cloud HD meeting service for high quality video conversations and screen sharing at work and at home. It is an independent (non social network) service, you can login with your work email, G,oogle Apps or Facebook. Please check out our customer testimonials http://zoom.us/customer/, try it out, and we love to hear your feedback.

We fulfill all your requirements except that we need a client install (PC/Mac/iPad and soon iPhone/Android) - check out http://vsee.com Here's how we fare against other players and could be useful for your research http://vsee.com/videoconference

Have you tried WizIQ virtual classroom? It offers 6-way video streaming, does not require any download and allows screen sharing. Looking at your requirements and having used it for long my suggestion will be you give it a try (http://www.wiziq.com/Virtual_Classroom.aspx%20)

Thanks Dugan for suggesting iMeet! You can see up to 15 people in HD video, but you can also connect with up to 125 people with web and audio while you share files, share your screen, or just chat. iMeet is also web based, making it easy for your participants to join the conference! You can even try iMeet for free today at http://www.pgi.com/imeet

If you look for conference call, Skype offers a great solution. Otherwise, the new sookooroo (http://sookooroo.com) offers all the business collaboration tools you mention. No downloads. 8 people video. 200 participants. Instant and effortless invitation. (I'm co-founder)

I am part of a team that uses Visimeet(http://www.iocom.com) on daily basis for our collaboration. 8+ people, with screen sharing. It is available on Windows, Mac, and Linux. Video and audio quality is great, We are developers spread across the US(and EU). Granted, we are the team that develops Visimeet, so we are biased :) but it works great for us and any problems that occur we fix promptly because it first annoys us. The nice thing is that Visimeet is *NOT* peer-to-peer, but rather our collaboration servers(on different continents) are federated together via fast connections; so the meeting has great audio/video quality even for very big distributed teams. Check it out, you can always uninstall if your don't like it. Oh and we just released the webclient, so you can also join a meeting from Chrome.

Google hangout is great http://www.google.com/+/learnmore/hangouts/. You might want to have a seperate google account for work vs friends.