EA has released a trial version of Battlefield 4 via their Game Time program. Titanfall was previously available and SimCity released earlier this week with a 4 hour trial.
The Battlefield 4 release offers a more kindly 168 hours (1 week) of access, however you must download it from Origin this week as it will not be available after 14th August. The timer starts the first time you play, so you could download it now and play again in 3 weeks time if you want, as long as you don’t load the game once it has downloaded.
Should you decide to try Battlefield 4 and then buy the full version, your progress carries into the full game.
Battlefield 4 is currently available in Europe but not on the North America Origin suggesting they are releasing it in different areas at different times.