Never had a VPS before but I was wondering if I got a linode, would I be able to upload a program I made and run it?

If it is written and compiled for the right OS, then yes you can upload a program you made. However, exe is a windows executable. Linode does not offer a Windows VPS.

There are programs for executing Windows apps on Linux (wine), but if you are writing the application, your best bet is write it for the OS that it is being used on.

If it's written in VB.NET or C#, then mono might be able to run it. That is, assuming it doesn't have a GUI (afaik, mono doesn't give you Windows.Forms) or other Windows-specific code.

Dang, I was actually going to write it in C++. It's basic console, nothing too complicated. Anything for C++ ?

There's a C++ compiler for Linux (g++). If the code is portable you can just use that to make a native Linux executable.

Can it support all the standard libraries and the SDL networking library?

Yes. SDL actually originates on Linux, you know. And "standard" C and C++ libraries are inspired and originating from Unix too.
There's a port of the whole GNU dev chain (gcc, g++, binutils) to Windows, called Mingw32, if you want to experiment on a local machine first.