If you already have an application written in .Net, you can scan your application with the Mono Migration Analyzer (MoMA) to determine if your application uses anything not supported by Mono.

The current stable release version of Mono is 3.2.3. The previous stable release was 2.10.8 (released December 19th, 2011), which is not supported anymore (because its branch doesn't receive more backports).

The easiest way to describe what Mono currently supports is:
Everything in .NET 4.5 except WPF, WWF, and with limited WCF and limited ASP.NET 4.5 async stack.

Here is a slightly more detailed view, by .NET framework version:

Implemented Partially Implemented Not Implemented

.NET 4.5

C# 5.0 - async support
Async Base Class Library Upgrade
MVC4 - Partial, no async features supported.
ASP.NET 4.5 Async Pipeline - Needs an parallel processing pipeline with async support, not done.

.NET 4.0

C# 4.0
ASP.Net 4.0
ASP.Net MVC 1, MVC 2 and MVC3
Managed Extensibily Framework - Shared with .NET via MS-PL license
Dynamic Language Runtime - Shared with .NET via MS-PL license
Client side OData - Shared with .NET via MS-PL license
EntityFramework - Available since Mono 2.11.3.
Parallel Framework and PLINQ
CodeContracts - API complete, partial tooling
Server-side OData - Depends on Entity Framework.

.NET 3.5

C# 3.0
ASP.Net 3.5
LINQ to SQL - Mostly done, but a few features missing

.NET 3.0

WCF - silverlight 2.0 subset completed
WPF - no plans to implement
WWF - Will implement WWF 4 instead on future versions of Mono.

.NET 2.0

C# 2.0 (generics)
Core Libraries 2.0: mscorlib, System, System.Xml
ASP.Net 2.0 - except WebParts
ADO.Net 2.0
Winforms/System.Drawing 2.0 - does not support right-to-left

.NET 1.1

C# 1.0
Core Libraries 1.1: mscorlib, System, System.Xml
ASP.Net 1.1
ADO.Net 1.1
Winforms/System.Drawing 1.1
System.Management - does not map to Linux
System.EnterpriseServices - deprecated

Current Mono Master

This section will be updated as major components are added to Mono after the latest official release.

For details on individual classes and methods implemented by Mono, please see our class status pages. Note that these are built from SVN versions and some methods may not be in a released version yet.