Sid Meier's Pirates is an absolute classic and seems to have been around for donkey's years, but it has arguably found itself most at home on the PSP where its simple charms fit best. As a wet behind the ears buccaneer, you'll start out in a small skiff with only a few deckhands, sailing around the Caribbean and trying to make a name for yourself through whichever means you like. Do you want to become a trader? Will you take the adventurer route and search for long-lost treasure? Will you hunt down the pirates for bounty, or become one yourself? The choice is yours.
You can pick up a copy for just £13.99 from Coolshop at the moment, although they're running somewhat low on stock so you'll need to hurry. The nearest price from a larger vendor we can find is £24.89 from Simply Games, although they've been out of stock for a while now. Startup Media, an Amazon/Play Marketplace merchant, is offering copies for £15.67 delivered but you can never be too careful with Marketplace vendors. Plus you'll still save yourself nearly £2.
Pirates! is a deceptively simple game at heart: you're let loose in the Caribbean with a few mean tools at your disposal and you have a few ways of making it big. You start out by picking your character's speciality (sword-fighting, dancing, navigation etc.) and their national allegiance (affecting how many ports you start with, and who you can and can't attack) and then you're pretty much left to your own devices.
There are a number of ways to both legally and illegally make your name upon the high seas, from trading resources Taipan-style to sacking enemy ports to going one-on-one with pirate captains with your trusty cutlass and then nicking their ships when you win. As you progress you'll not only be able to upgrade your own ship, but commandeer new ones, allowing you to take down people like Balckbeard and French royal treasure galleons later in the game.
Pirates! was the first game I ever actually bought for my PSP and it remains the one PSP game I take with me wherever I go. It's equally good for long travelling stints as it is for a quick five minute play on the fly and it has a huge deal of replayability. It's not quite as deep or rich as perhaps it could be, but it manages to offer easy accessibility and a challenge for the hardcore gamer with a dynamic playing field that constantly offers up ever-changing environments. Meier has been perfecting this game for two decades now, and I heartily recommend to grab a copy if you can.