The first Mass Effect set a precedent for the remainder of the original trilogy. Commander Shepard knew by the time they reached Virmire that the decisions they were often forced to make would highly impact the future of the galaxy. When faced with the task of choosing which squadmate was worth saving, there wasn't much time for Shepard to carefully consider the overall impact of that choice.
Knowing their lives were on the line, both Kaidan Alenko and Ashley Williams encouraged Shepard to save the other squadmate. As soldiers, they knew what they were signing up for when they joined the Alliance, and sacrificing themselves for the good of the team was all but a requirement.
A lot of players have been prompted to choose whichever squadmate they were trying to launch a romance with, knowing if their potential love interest died that's it for the relationship. There aren't a lot of romance options in ME1 to begin with, so it wasn't like Shepard could just move on and finish out the game with another lover. Interestingly, the reasons for choosing one squadmate over the other, romance intentions aside, tend to be very different.
Knowing where the Mass Effect trilogy goes after the first game, it's important to consider which of the two will be more useful as far as squadmates go in the final battle against the Reapers in ME3. When taking their abilities into consideration, Kaidan tends to be the more experienced soldier. He's physically stronger, which means he can take a much harder beating in battle. He's also got technical and biotic abilities that make him more versatile on and off the battlefield.
Having a soldier who knows what to do and how to do it without much direction makes him an essential asset against the Reapers, but it's not all sunshine and roses with Kaidan. One of the downsides to saving him over Ashley is that he will question Shepard's choice all throughout the third game -- especially if Shepard was romancing him. Did Shepard only save him because of the bond they were developing? That possibility weighs heavily on him, and there are no right answers when asked "Why me?" On the other hand, conversations with Kaidan are much more prevalent on the Normandy in ME3 than it is with Ashley unless Shepard is romancing her.
Kaiden may be the stronger choice, but Ashley isn't without her merits. Those who are looking for more character development and growth would be better off saving Ashley, especially if Shepard is romancing her. By the time of Mass Effect 3, Ashley has undergone a modicum of personal growth. In the first game, Ashley is incredibly xenophobic, and her dislike of alien cultures and beings is made more than clear. She doesn't like working with the aliens aboard the Normandy and she can be downright judgmental to the point of cruel if given the chance.
She has an intense hatred for Cerberus, though, which rubs against her prejudice in a strange way. Cerberus and the Illusive Man tend to be all about the survival and advancement of humanity above all else, but that doesn't sit well with Ashley. Perhaps it was seeing the extreme actions Cerberus took for the sake of humanity that started to change her mind. By the time the third game rolls around, especially if she's been hanging out with a Paragon Shepard, she's been through and seen enough devastation that alien lives start to matter to her in ways even she didn't think possible -- especially the crew of the Normandy.
Unfortunately, there isn't nearly as much interaction with Ashley in ME3 unless Shepard is romancing her. She's just sort of there, floating or moping around, and because Vega tends to be a much better tank than her, taking her out in battle isn't really necessary.
As Shepard's fellow humans, a lot of players struggle with this decision, and not because they particularly like Kaidan and Ashley. Many are more interested in the lives of and interactions with their alien squadmates, who tend to have far more personality throughout the trilogy. Unfortunately, this makes the human squadmates somewhat bland by comparison. That's why making a decision to save one human squadmate over the other tends to be so hard. If it was Garrus, Tali, Wrex or Liara in place of one of the human squadmates, sacrificing the human would be much easier to live with. Even then, though, Kaiden is the much better choice of the two, if only because he better fleshes out the Shepard the player takes into the finale.