The RosettaCommons (external link) (the group of labs that maintain Rosetta) maintains a number of servers for free public academic use (external link). Servers for commercial use are also availible from an external provider.
ROSIE (external link) is a server that offers several (14) Rosetta applications through a simple web interface. It is perfect for use by those new to Rosetta. Instead of dealing with Rosetta command lines, you are presented with an web page GUI for each application. Filling in the web form provides the server with the data it needs to run your Rosetta job. Despite ROSIE's variety it offers only a slice of Rosetta's full functionality, depending on what applications users have written web front-ends for. Because this is a free public resource, computer time is limited. ROSIE runs can be downloaded and used to build Rosetta jobs that you run on your own local resources.
ROBETTA (external link) (Robot-Rosetta) is a server that provides ab initio folding and structure prediction, as well as fragment selection for local runs of Rosetta. This is the oldest Rosetta server, set up to provide for Rosetta's original functions. It also provides interface alanine scanning and DNA interface residue scanning.
The PIPER-FlexPepDock server provides access to Rosetta's global docking of a peptide onto a receptor (where the binding pocket is unknown).