Hi there Mr Salt
Short answer is yes, they can take your ship, but there are caveats.
Once your ship is taken (or blown out of the water <img src="style_emoticons/<#EMO_DIR#>/rolleyes.gif" style="vertical-align:middle" emoid="

" border="0" alt="rolleyes.gif" />) you are sent back to the nearest port of your nation. You may or may not have lost your ship permanently - please see below.
Only Pirates can actually "take" a ship from another player or computer controlled opponent. They can do this once every two hours. All other classes must leave the ship they have boarded behind, but they can take the ship's "Pennant" after Level 5 and if they have invested in that skill. A certain number of pennants collected can be exchanged for rewards - including ships - at your nation's capital. It goes without saying therefore that all Non-Pirate classes must buy their ships or get them via the Pennants award system (which is actually rather too much hard work to be worth it...).
You can only fight human players in areas designated as PVP enabled (unless you actively want to PVP - see further below). This happens when there has been enough "unrest" caused around the environs of a particular port. The more unrest there is (basically the more fights there are going on) the bigger the PVP area. Often they all overlap so extremely large areas of the Caribbean can become PVP. When that happens then the only really safe areas are those around the various nations' starter ports.
When you buy a ship it generally has 5 "Durability" points (I am assuming a good quality ship here - they vary depending on who built them). Each time you lose a fight then that ship loses a durability point, until eventually you lose the ship altogether (otherwise it's magically back in your dry dock when you get back to Port). However you can refill those durability points at any time if you happen to have a ship deed of the same type in your inventory.
A ship taken by Piracy however only ever has ONE durability point - so it can be taken away again permanently. You can keep taking them, so you can have a large supply instead of just one with five points on it but of course if you then invest money in outfitting one of those ships then you can easily lose quite a lot of investment in one go... The other thing is that if you happen to take a ship which is above your theoretical level (i.e. you would not be allowed to buy it legally until you are high enough level) then you are automatically given PVP Enabled status (you get big crossed swords appearing above your ship to other players) when travelling in that ship - and that's everywhere! You tend not to hang on to those ships very long.... however, being a bit rubbish at it I have not yet taken a ship too far above my class.
One last thing, if you are in to PVP then you can enable your PVP flag for combat anywhere anyway if you like. However, as with all PVP MMORPGS I suspect a lot of bullying goes on - I have been chased by people dozens of levels above me, which is fun when you are in a small ship that can escape relatively easily (if the wind is in the right direction and an island doesn't get in your way...) but not so much if you are in a ship on which you have lavished time and money. Moral: Don't go into PVP areas if you are afraid of losing your ship.
One thing I think would be a good idea would be to go the "World of Pirates" way and have those who's ship has been taken placed on to a small slow raft on which they have to make their way back to port....
Anyway, I hope I answered fully enough.