I keep some data on an FTP server.
Can I conect with ArcMap 10.1 to use this data?
Yes, you can but it really wouldn't be recommended.
Here is a really good post on ServerFault about mounting a FTP server connection as a local drive; you can then set this as a connection in ArcCatalog that you can use.
Be aware that when you open some datasources remotely that network/connection performance can be a severe impact on stability. If that connection crashes; you run the risk of having to clean-up the temp files.