When you say "Will Google count it as a link", technically, it will be a backlink. Yahoo site explorer will count it in your number of backlinks, etc.
However, in terms of passing pagerank (link juice), it will not double the amount of pagerank passed to the page.
To do this for the purpose of manipulating pagerank, or getting your page indexed for a term (i.e. the different anchor text) is not a proper practice.
If you do it because it happened to be that way (you linked from your blog to another page twice, with different anchor text), then that is fine.
Does this help?
Lets say I insert two links on one page ( page1) of my site pointing to another page of my site ( page 2), with different anchor text.
Does Google count two links to page 2 from page 1 or just a single link ?
Its a good question, if you consider google then it might count only 1 link. and yahoo will consider it as a back link. Google sometimes count it as back link. There are many spammers who just give links on same page its short term give boost.
Anchor text helps, but its not the most important thing...
So basically, if there is a purposeful use of having 2 links to the same url, then you can go ahead and do it...
But if your doin it to play the system, it won't do what you think it might...
Could this be considered grey or black hat SEO? Canada Fred, any thoughts?
It's perfectly OK. It's your webpage and you can do whatever you want with it. Maybe the web page will need to do something like this ten times or more. It is often a completely natural occurence. White hat all the way (it works pretty good too).
I just wrote about this ethical SEO technique more in depth (in my signature for ease of reference: Anchor Congruency).