Not necessarily Indian. But from across the globe.
For example, some analysis abt how Vikram Pandit will be do as the new CEO of Citigroup, analysis of the sub-prime mortgage crisis, which companies profited (Goldman-Sachs for one), which lost (Citigroup, obviously :P), how much they lost of made, etc…
And yes, they should be free.,…many of the sites ask you to register by paying a few dollars. Not interested in that.
I am not interested in “what stocks to buy” etc… type of articles.
In most of the sites like Forbes, Bloomberg .. etc. News is always free but the analysis part is payed.
Good thing to try is, if you have a google account, go to iGoogle and click on “add stuff” on top right corner. In the selection page select on Finance. you will get a huge list of such sites with latest news. Add which ever you like to your gadgets page. After a few days you’ll get an idea on whats good and whats not so good.
Hope this helps
Although I am not really that interested in Finance, one site I find really interesting is Fool.com: Stock Market Advice | Stock Investing Advice
They present a dry and boring financial news also in a fun way (you can guess from their name .. they call ther readers Fools 
). And they always have interesting self-help articles about maintaining your personal finances too.