Can I program for Arduino without having a real board?
There are a whole slew of Arduino simulators out there, many free, and some paid products as well.

The CodeBlocks Arduino development environment includes a free Arduino simulator, still under development but functional.
Simuino simulates the Arduino Uno and Mega pins - not a pretty-looking realistic simulator, but it works.
The Python based Arduino Simulator is another option, that plays well with the official IDE
Virtronics Simulator for Arduino looks promising, but I don't see why I would pay $14.99 for it, when I could buy one or more actual Arduino clones for that price

Many other Arduino simulators are out there if you search, and new ones are being announced, even crowdfunded, all the time.