The latest official version is 0.9.11
If you are confused by these choices, then you definitely want one of these. If you are still confused by choices, then pick the first one. If you are still confused, then you need to pick a different hobby.
The rest of you may want to choose one of the following:
The latest SVN versions are at Orphis’s DeSmuME BuildBot These are not officially supported for gaming, and you shouldn’t use them unless you know what you’re doing.
And there may be other interesting things at the: