Instead of writing my ASP.NET C# applications in Visual Studio, I used my favorite text editor UltraEdit32.
Is there any way I can implement MVC without the use of VS?
There is nothing VS specific with the MVC framework - it is just a bunch of DLLs that you can use. The wizards in VS just build you a quick-start framework.
ASP.NET MVC is "bin-deployable" - there is nothing too clever to set up on the server either - just point the wildcard ISAPI filter to ASP.NET
Assuming you have the correct assemblies and a C# compiler you in theory can use whatever you want to edit the code and then just run the compiler by hand or using a build script. That being said it is a real pain doing .NET development without Visual Studio/SharpEdit/Monodevelop in my opinion.
Even if you didn't want to actually edit in VS, you could create the project there and edit the files in another editor.
For small to mid size mvc project WebMatrix is not bad at all. Also for simple changes to the projects I often use SublimeText.