These are some of the major libraries that you can use:
- Gtk#, the Cross platform GUI API Unix, Windows, MacOS X,
- this is an entire stack of libraries and includes widgets (with Gtk+), Accessibility and international text rendering (with PangoSharp).
- Mono.DataConvert - System.BitConverter implemented correctly, and well designed.
- Mono.Addins - Extensibility Framework, similar to MEF.
- Mono.Cairo - Cairo Graphics Binding.
- Mono.Cecil - ECMA CIL Image Manipulation.
- Xml.Relaxng - RelaxNG parsing and validation.
- Novell.Directory.Ldap - LDAP libraries.
- Daap.Sharp - An implementation of the DAAP protocol
- (Music exchange protocol, you can consume or expose music sources)
- Mono.Upnp - Universal Plug and Play implementation in managed code.
- Mono.ZeroConf - Cross platform ZeroConf/Bonjour API for .NET apps.
- BitSharp - Bittorrent client/server library, now called MonoTorrent
- Mono.Nat - Network Address Translation.
- Mono.Rocks - Useful Extension methods/Functional features for C#, now superseded by Cadenza
- SmugMugSharp - Bindings to talk to SmugMug
- Crimson - Crypto libraries beyond what is available in .NET
- Mono.WebBrowser - Wrapper for Firefox or WebKit.
- WebkitSharp - Bindings to use WebKit from C#
- GtkSharpRibbon - The Ribbon, implemented in Gtk# (cross platform)
- IPodSharp - Library to communicate and manipulate iPods.
- TagLibSharp - Library to annotate multimedia files (tagging).
- Exiv2Sharp - EXIF reading/writing library.
Linux Specific:
- Mono.Posix/Mono.Unix.
- NDesk.DBus
- Mono.Fuse - User-space file systems.
I am sure I am missing a bunch of other libraries.
Most of these (and many more) are linked to via the Libraries page.