In many campaigns it's just not an issue. The races all have access to Common, so they can communicate, and all gather in large cities or live under one king (or even a group of allies nations). While having three or four different races in a group may not be the norm, it's no more unusual than seeing an American, Canadian and Mexican all working together.
In other games if you need an excuse, come up with one. I recently played in a World's Largest Dungeon game that had a gnome, a dwarf, a half-ogre, two humans, an elf, and a half-orc -- all from different cultures (from tribal barbarians to Asian-themed). However, the DM had made the dungeon a mystic place you could stumble into from many different underground portals around the world (and of course once in, you couldn't get out). The characters were the survivors from numerous different expeditions that had gotten stuck within the dungeon, and naturally gathered together as a matter of survival. This workled well, and allowed racial tension to be played out if we wished, since there weren't many options for walking away without risking your life.
If you have to force unlikely characters together to start a campaign, just steal ideas from Shogun, The Magnificent Seven, Gladiator or The 13th Warrior as needed. Once they've played through an adventure, hopefully the characters have built enough trust and friendship to stick together despite the social norms.