Will my 32-bit application works, if i move my SQL 2000 Database to SQL 2005-64 bit running on OS 2003 64 bit? What are the advantages of moving to 2005 64 bit?

There are numerous articles on the WWW regarding the advantages of 64-bit environments that can be Googled, perhaps the most relevant article for your specific question is http://www.microsoft.com/sql/editions/64bit/overview.mspx 

In short, 32-bit applications are only in danger of failing if they are installed and run directly on the 64-bit hardware itself. If your 32-bit application is running on a 32-bit client computer and is merely connecting to the 64-bit SQL server instance, then everything should be fine.

I have encountered one notable difference between 32-bit and 64-bit SQL server versions when using older Visual Basic connection strings from VBscript files or "classic" ASP pages, in that connections to 64-bit instances require a SQLOLEDB connection: 

When connecting to 32-bit versions, it was possible to use this syntax:

Set Db = CreateObject("adodb.Connection")
Db.ConnectionString = "driver={SQL Server};server=<ServerName>;uid=<username>;pwd=<password>;database=<databasename>

The same connection to a 64-bit instance requires a change: 

Set Db = CreateObject("adodb.Connection")
Db.ConnectionString = "Provider=SQLOLEDB;server=<ServerName>;uid=<username>;pwd=<password>;database=<databasename>

Hope this helps.

difference between 32 & 64 bits.

Thanks for the answers Satya. I have gone through the provided links and they are very helpful.

http://download.microsoft.com/download/a/4/7/a47b7b0e-976d-4f49-b15d-f02ade638ebe/Adv64BitEnv.doc