Lots of new services coming online for a fee, of course. You can get some free previews though. For example, Footnote has an “interactive” 1860 census online. Dimitri pointed out that you can download the non-interactive version for free here.
Another one I found that was searchable was the family search website. Their FREE 1880 online census helped me find and locate a lot of soldiers for my book after the war.
If you’re looking for a searchable archive with letters and diaries, you have my soldierstudies.org, which is free, and Alexander Street Press, which is free now, but will be pay-per-view soon. [Note: there are some issues with the accuracy of ASP, but it is a cool site with a lot of features!]