The way to set "source breakpoints" on the Arduino is to add a serial output to send the value the you want to see to the Serial Monitor.

When you are ready the next step is to move to WinAVR, AVR Studio and a Atmel JTAG Mark II or a Atmel Dragon.

These programs and devices will allow you to create C code and single step through the code and monitor variables and registers. The JTAG devices can single step through your C code or the assembly code created by the compiler.

Be forewarned that high level embedded C programming is still very close to the machine and you have to be careful single stepping interrupt routines, timer routines and other low level routines because many times it will prevent the code from operating correctly.

The Visual Micro plugin for Microsoft Visual Studio 2015 Community Edition (free) provides a USB debugger for Arduino. It allows you to do exactly as you describe. (don't forget to click to install C++ during Ide install)

The debugger supports Serial, RF, Bluetooth and some WiFi. It enables the values of variables to be watched or update while the Arduino runs. Chart and data/pin visualizations along with watch, trace, break are included.

news: January 2016 also includes release of a Gdb debugger for the Arduino Zero. As with the Serial/Bluethooth debugger, the Gdb version supports ino/cpp source code but additionally supports debug of Arduino core and libraries. Supports many features such as:- step over, step out, step instruction or source line, memory, registers, locals, watch, live expressions, stack trace.

For inspecting variables I just print them to the serial monitor. Here's an example I'm working on at the moment:

Serial.println(String(index) + " : " + String(total) + " : " + String(average));