A friend thinking of getting into Eve asked "If I choose a race other than Caldari, can I still hang out with you if our races are at war?"
Short answer: Yes.
There are four playable factions (aka races) in Eve and several non-playable ones. Each of the four factions has three bloodlines to make 12 options for your character when starting. The four factions are called Amarr, Caldari, Gallente, and Minmatar. The first two are allies, and the last two are allies, and each alliance does not like the other. In fact, the Caldari and Gallente had nasty war a while back before the modern era, and the Minmatar used to be enslaved by the Amarr before they rebelled.
However, all this bad blood in the current Eve storyline has been settled down such that the factions have no open warfare against each other. Think of it like the Cold War: lots of little flare ups fought by proxy agencies or black operatives, and lots of build up of fleets, but no open fighting.
What this means for players is that choosing a faction and a bloodline only really impacts your starting region and skills. For example, a Caldari newbie would have Caldari Frigate IV and Missile Launcher Operation IV while a Minmatar starting character would have Minmatar Frigate IV and Small Projectile Turret IV (depending on schools and profession picked) but from there both characters are free to train any factions ship skills and any weapons. Similarly, they could pick up and leave their starting region and go to any of the other four factions' regions to live there. They will suffer no ill effects except perhaps finding their equipment and ships at a higher price due to availability.
However, if you run missions for a NPC corporation, sooner or later you will be assigned missions that pit you against faction Navy NPCs of the rival faction of the corporation agent's faction. Heh, confused? Basically, if you run missions for a Minmatar agent you will have some missions where you are fighting Amarr and/or Caldari navy NPCs. These missions cause your standings with the Amarr and Caldari factions to fall while they rise for Minmatar and Gallente. Eventually, if you run enough missions your faction standing will fall so low that their NPC police units at gates in their space will attack you (although the attacks are pretty lame).
This is all well and good, but for 90% of the Eve population it is meaningless. Why you ask?
Because its the player factions that mean so much more.
There are several major player factions in lawless space and two of the largest, GBC and Red Swarm, are in the midst of a massive war that has been going on for months if not a year. Kill on sight rules the day in their space followed by NBSI: not blue, shoot it (allies and friends are marked with blue symbols on the screen, enemies red, neutrals with nothing. NBSI means treat all neutrals as enemies).
So my point is that until CCP releases some form of Factional Warfare between the major NPC factions, it won't matter whether you pick Amarr or Minmatar for your character unless you are big into roleplaying.