In Baldur's Gate (1 & 2), it is more than possible that a devious player may have killed a character before they have divulged plot specific information. In these cases, a robed character named "Biff the Understudy" will appear and say the required lines. Furthermore, Baldur's Gate II features the character Arkanis Gath, who will appear and instantly kill off your party if you for some idiotic reason attack a plot-sensitive NPC and make it impossible to proceed with the main story. You can't save once he appears either, so it keeps you from screwing up.
Also in Baldur's Gate II, if the player is an elf named Drizzt with low reputation, then when you meet the actual Drizzt Do'urden he'll challenge the player for the honor of his name. Likewise, if, in BG1, the player kills Drizzt and takes his loot, he'll recognize it as his when and if he meets the player in the sequel, and will be more hostile than usual. To solve this, you need to not have his weaponry on you when you meet him - that includes the offending player temporarily dropping the kit before you meet him. The same if you just steal the swords.
A sidequest in the first dungeon of BG2 gives a + 2 greatsword as the reward which the item description identifies as Sarevok's weapon from the previous game, greatly depowered by his death. Keeping hold of it until you can recruit Sarevok in ToB (long past the point where it's been superseded by better weapons) nets the player some extra dialogue and repowers it to a respectable Infinity–1 Sword.
During a heavy rainstorm, there's a chance CHARNAME or a party member wearing plate or full plate will be struck by lightning. Very surprising the first time it happens to you. It can happen if a character is wearing splint mail armor as well. And if you have more than one character wearing it, they can all be hit in a short amount of time. Good thing it doesn't do any damage, though.
Though BG2 is designed to be played with a party of six, there are a few (though not many) places where the developers acknowledge that there can be solo playthroughs, for example when you are dragged down to hell it says somethings along the line of "as you fall, you feel a force pulling around you. If others had fought with you, they might have been dragged down as well, but you are alone."
In the expansion, Forgotten Realms historian Volothamp Geddarm will offer to read a profile on any of your party members. A character traveling alone has the option to say "Clearly I'm not traveling with anyone," or something along those lines.
In the first Baldur's Gate, your party will encounter a pair of assassins early on who will issue a threat and then walk away and disappear from the zone. They are strong enough that they will usually be able to get away even if your party attempts to engage them. Later, one shows up again with the news that his companion managed to secretly poison your rations, and he offers you half of the antidote in exchange for an item to break his geas. Trying to kill the first poisoner when he shows up again but before he gives you his half of the antidote will effectively break finding the cure, making the game Unwinnable and causing your party to die in ten days. However, if your party is able to deal sufficient damage to kill both of the characters at their first meeting (multiple wands of fire and necklaces of missiles help substantially), the quest will never be triggered (not even by a Biff the Understudy).
In Chapter 6 in Shadows of Amn, a gnomish NPC in the Underdark caves leading to Ust Natha asks you to take care of a demon that's been terrorizing his men before he'll give you a "Light Gem" that will allow you access into a specific cave to continue the plot. You could complete his task normally...or you could just get Imoen to pickpocket the NPC and go into the cave yourself. Once you get to the creature in the cave, the silver dragon Adalon, she specifically calls you out on skipping the mission and not killing the creature. Adalon also notes if you decide to skip the entire Ust Natha questline (and subsequently not bother to get her missing dragon eggs back) and go directly to the Underdark exit through the Kuo-Toa Lair.
You can get the Light Gem by killing the NPC and taking it from his corpse. Or you can pretend you did his mission - he asks you to fight a monster and then collapse the hole it came from. If you skip the fight and just collapse the hole, you later get a message that the gnome settlement was slaughtered by the monster, which dug its way back up.
in the Enhanced Edition of Baldur's Gate, having Edwin in your party when you do Neera's recruitment event will actually let you skip the fight with the red wizard and his lackeys after neera. Because after Neera teleports Ekandor who knows where Edwin is the highest ranking red wizard there at the moment and says attacking him would be a grave offense, and so they leave your party and Neera be. Edwin will then refuse to stay in the party with Neera... because he found out from the event that she's wanted by the Red Wizards. If you recruit them the other way around, he's not around for it and so is simply generally Edwin-arrogant about her.
In the second game, if the Player Character is male and romancing Jaheira, there will come a mini-side quest in which she is held hostage by bandits. You can offer to trade her safety for yours, and the bandits will agree, before deciding to double-cross and shoot you. This arrow will always deal 50% of your health, but if you happen to be equipped with a Shield of Arrow Deflection, the arrow bounces back and usually kills the leader, making the fight much easier. A stoneskin spell will also No Sell it, because it counts as a physical attack.
If you have the drow Viconia with you to the Underdark, she will function as a guide.
In the first game, if you chose to attack Helshara, Ithmeera and Delorna instead of using your thief to get the items needed for Alatos' quest. Their father, Shandalar, who is at Ulgoth's Beard and has a quest in the expansion pack, will automatically teleport you to Ice Island without speaking to you (probably in the hopes of getting you killed) when you approach him. If you did not kill his daughters, he will instead speak to you and tell you about his quest. If you accept, he then teleports you to Ice Island. Note that after doing his quest you can go back and kill his daughters anyway, because he disappears from Ulgoth's Beard once it's done.
About three-quarters of the way through the first game, you encounter the Big Bad in disguise. If you solve the Significant Anagram of his name and decide to kill him off early (your characters are likely powerful enough to do so by this point), you'll find that he, uniquely among characters in the game, is immune to all damage.