Reading the responses, I couldn't help but be irked by the support for this 'holy trinity' party requirement. Where you typically have the fighter that takes hits and deals no damage, the rogue who murders everyone and picks locks but is a glass cannon, the wizard that torrents endless waves of flame and energy but is also a glass cannon and the cleric that heals them. When did this become standard? Did MMOs do this?
I agree that the tank/DPS/healer trinity is an abomination that needs to die.
Still, regardless of the game or system there are usually certain roles that you'll want to fill in your party. You almost always need a character that can patch your party up after a tough fight. You'll want a character that can open locked containers and disarm deadly traps. If the game has magic in it, you'll want to have a mage since they are usually the most powerful characters around, and you may end up facing enemies with protection spells that can only be reliably dispelled by another magic user. Straight-up fighters are utility characters that you'll want to have around for numerous reasons, for example because your mages are probably squishy and don't necessarily have an unlimited supply of spells.
Depending on the system you may be able to fill these roles with a varying number of characters, though. Perhaps you have a multiclassed Fighter/Thief that can open most basic locks while still being adequate in combat. Or perhaps you'll use your mage instead, giving her spells that allow her to open locks or turn herself invisible. Or perhaps you leave the fighter out of the equation entirely and instead turn one of your mages into a close-combat monster with the correct buffs and items. Rangers might be able to switch between melee and ranged combat while being effective either way, and clerics and druids could serve multiple purposes, using a varying degree of defensive and offensive spells as well as traditional weapons, perhaps replacing basic fighters or even mages to an extent. This means that even with a party size of four you might be able to do some interesting stuff, rather than just having a fighter, thief, mage an cleric with you, each serving their one and only possible role.
On the other hand, especially with newer games the systems tend to be very rigid, with each role tied strictly to a single character, which also makes small parties much more boring. Mages are often mostly just damage dealers and/or healers, lacking effective protective spells as well as useful utility spells (like ones that would allow them to open locks). This means that you'll need a fighter or two to protect them. Clerics often don't even exist, but if they do, their role is usually to strictly cast buffs and/or healing spells, with little room for other things. And then you've got
thiefs rogues, who'll deal more damage than anyone but need those fighters to keep enemies from attacking them. As a result four-character parties tend to become very dull, as you need a different character for each role, and even though there may be a few different paths you can take with each character (like choosing whether you want your rogue to use daggers or bows, or which weapon you want your fighter to specialize in), it tends to make all parties feel more or less the same.