During the events on [Virmire] you’ll have to choose between rescuing Ashley or Kaiden.
Choice: Save Ashley or Kaiden
As you explore the base on Virmire, you’ll have to send either Ashley or Kaiden to work with some Salarians led by Captain Kirrahe. This choice doesn’t matter too much, but if one of them is a core member of your squad, gameplay-wise, do not send them, as you won’t be able to bring them with you. Obviously.
Later on you’ll conspire to destroy the base on Virmire by the means of a bomb, which is delivered by the Normandy. The human squad member whom you did not send with Captain Kirrahe will arrive with said bomb and stay behind to arm it, after which you’ll get a distress call from the squad member you sent with Captain Kirrahe, who is pinned down in an AA tower. En route to the AA tower you’ll be informed by the squad member guarding the bomb that Geth are attacking their position and they’ve armed the bomb to ensure it goes off.
This leaves you with one of the more important choices in Mass Effect: do you relieve and rescue Ashley or Kaiden? It doesn’t matter which one was sent to the AA tower with Captain Kirrahe and which one was left to arm the bomb, this plays out the same way. You only have time to save both, and whomever you neglect will be killed when the bomb destroys the base on Virmire.
The consequences here are pretty obvious and immediate: Either Ashley or Kaiden will die, and will remain so for the rest of the trilogy. Only one zombie allowed on the Normandy, dammit!
Obviously this means you won’t be able to romance the dead character, nor will you be able to take them with you as a squad member. Turns out vaporized corpses aren’t really good for much.
In Mass Effect 2 you’ll meet up with the survivor, but they’re not a possible romantic interest or squad member in this game.
In Mass Effect 3, the surviving character takes a more active role, albeit their overall contribution to events varies significantly based on later choices. You’ll get them for one mission at the start of Mass Effect 3, after which various choices will determine whether they perish, become a War Asset, or once again rejoin your squad and become a possible romantic interest.