Arduino Mega: which Digital pins are already used for something?
Don't worry about the led on pin 13, it just sits there but doesn't block anything. 

You can still use the pin as a normal IO pin.

You didn't mention whether your 30 inputs are digital or analog, so let's have a look at digital input first.

I have never used the MCP23017 mentioned by Martynas, but the linked article looks very interesting and I'll definitely order one of these amazing chips!

Another option might be using 8 bit PISO (parallel in - serial out shift registers, such as the 74HC165. Consider this as the complement to the 75HC595 for output. These shift registers are dirt cheap (around 0.3 €), are available as DIP (important for breadboarding) and can be run via SPI. 

Advantages: 


it's fast to read in 8 digital lines into a byte (why would one want to use more than a bit for the state of a digital input?)
the shift registers can be daisychained, subsequent calls of ShiftIn allows to read all (digital) input states into a corresponding data structure (array of bytes, etc.) using just three pins on your Arduino.