Party size does not affect loot drop quality.
Your drops are individual and the same as if you were solo.
1 Drops are different for each party member, increasing the probability of more relevant or interesting finds when discussed, shared, and traded between a four-person party.
gaming.stackexchange.com/users/21177/Wolf
As sean said, party size doesn't directly affect the loot - but there are indirect effects: monster hp only increases by 75% per party member
so you'll get more monsters down in the same time compared to playing solo.
more mobs means more loot and thus more chances to get good items.
in other words: playinng in a (good) group increases your "good items per time"-ratio, but doesn't change the "good items per mob"-ratio when playing with friends/talking with your party members about their loot, chances are high someone else gets an item you need (and other way around), so you can trade items.
in other words: when discussing and sharing items, your chances to get good items increase a lot (up to 100% per additional party member), because everyone gets as much loot as he would get solo.
the overall loot quantity is [count party members]-times as high.
gaming.stackexchange.com/users/9892/oezi
Edit: the things below are not correct anymore.
Since 1.04 magic find is individual for each player.
Source
Old answer
I'm not sure if that got changed again but as I've read it if a player with let's say 50% magic find joins the party, that magic find gets distributed over the players (So they player with MF actually ends up with lower MF than he has on his gear).
So party size CAN directly effect chance of better loot if a player with mf joins your party.
Not a blizzard source but where they talk about that Solo vs Group Magic Find Runs Here a Blizzard source Follower + Gold + Magic Find Equipment
gaming.stackexchange.com/users/20041/Philipp
According to the article posted and from what I have read the magic find % is added together and averaged over the group.
Ex: player 1 has 150% MF, player 2 has 75% MF and player 3 has 40% MF, the three are added together for 265% and averaged for a total of 88.3% per player in a group.
But according to the article the MF% is only added together if you are soloing and have a follower.
So if you have 150% MF and your follower has 150% MF then it is totaled at 300% for you, if I read the article correctly.
gaming.stackexchange.com/users/28824/Dragoon709
As of patch 1.0.8 .
Party size affects loot positively.
You get a buff called "Strength in Numbers".
Feel free to party up and get extra loot.
Players now receive a 10% bonus to Magic Find, Gold Find, and Experience per additional player in a multiplayer game, up to a maximum of 30% in a four-player game
gaming.stackexchange.com/users/6842/prolink007
I know that it  increases monster HP , and that experience and loot gained are separate from other party members, but do we have a higher chance of obtaining rare loot from having a larger party?
Does party size affect chance of better loot?
gaming.stackexchange.com
<diablo-3>
gaming.stackexchange.com/questions/64047
gaming.stackexchange.com/users/24469/mombi
Party size does not affect the loot. Players can receive a bonus to Magic Find, Gold Find and Experience per additional player. It seems like group size does not affect directly the chance of better drops.
The community is detailing how loot is affected by the size of a party.