I've heard of networks which offer you 3 way link exchanges with other site. Does google frown upon or allow such networks
You should read through Google's Webmaster Guidelines thoroughly if you have questions on this. They specifically say: "Don’t participate in link schemes designed to increase your site’s ranking or PageRank." Google's algorithms can detect 3-way exchanges pretty well by now.
I completely agree with WebGeek182, BUT good quality 3 way link exchanges do improve your rankings in google, so it looks like they are allowing them at present.
They may only help temporarily... If you have one here and there, and it's natural looking, you're probably fine, but as a general strategy, it's like playing Russian roulette with your site...
The main question is:" are sites in same category?". If sites has similar content and they are in similar category three way links exchange could be useful.
People have been saying this for years, and it does apply to people clicking on your link, but as far as search engine rankings are concerned off topic links still have a positive effect.
What's the point of a 3-way link exchange? I have an NFL-related site so I will do link exchanges with a few sports related sites. I'll get offers from sites to add, say their racing link and they add my link to their Golf site ---- and it will come from a athletic shoe site!, My thinking is, "I'll add links to the racing site, the golf site and the shoe site, and you give me a link on all three of your sites." What's the difference??
Many people believe google is now viewing reciprocal links as being of less value than one way links. 3 way linking gets around this problem, as all the links are one way only.