Without a doubt, the premier resource for genealogy research in Indiana, the Midwest, and the eastern United States is the Genealogy Center of the Allen County Public Library in Fort Wayne. I wrote about the opening of the new facility here and here. However, believe it or not, they don't have 'everything' for the local researcher (sorry Curt). So, if you're doing research on folks in Indiana you still need to go to the local libraries, court houses, and museums.
The Huntington City-Township Public Library in Huntington, Indiana has an excellent Indiana Room. Unlike most of the other libraries in the area, they have a librarian assigned to the Indiana Room so there is someone onsite to help with questions. The hours for the Indiana Room vary so you need to call to make sure it is open. In addition to resources specific to Huntington County, such as microfilm of county newspapers, files on local businesses and industries, school yearbooks, City and County Directories dating from 1892 to the present, they also have a collection of books from states east of Indiana.
The Kosciusko County Historical Society has a very good Genealogy Room. In addition to the "normal" books that you'll find on local history and families are some original record books. The Genealogy Room is located at the Historical Museum but does not have the same hours. The Kosciusko County Indiana GenWeb is an awesome site put together by Gene Andert.
In Whitley County, the Genealogical Society has a small research room at the Historical Museum, which was the home of Vice President Thomas R. Marshall. The Museum always has nice exhibits. The staff and volunteers are very helpful. The Whitley County Archives house the older original records such as estate packets, marriage records, etc. The Peabody Public Library has microfilm of the Columbia City Newspapers and a complete set of census records on microfilm. The South Whitley-Cleveland Township Library has the South Whitley newspapers on microfilm as well as an extensive obituary file and lots of other local resources.
And then there is the Indiana Historical Society and the Indiana State Archives and the Indiana State Library Genealogy Division, all located in Indianapolis. I attended a one-day workshop at the Historical Society and took a tour but have not actually done any research there. I've heard that all three are very nice and hope to find out for myself someday!