Instead of choosing just one side mission, I'm going to list my favorite one from each game, which is a more doable task than narrowing it down to just one throughout the whole series.
Mass Effect 1
|Talitha in "I Remember Me"|
Via Mad Maiden
Shepard,It actually reminds me of when I worked at the Department of Human Services. A nineteen-year-old girl came into an interview with me, very nervous, and when she refused to explain how she was paying her rent, she nearly broke down into tears. She then just started babbling, saying that yes, she did turn tricks, but she never put her babies in any danger. I took a deep breath and told her, "Okay, here's what we're going to do. I'm going to set you up with a three-month certification period for your food stamps and Medicaid and get you an appointment with our Families First department, so they can help you get a job. But until you do get a job, I need you to keep receipts. Or a ledger. It doesn't really matter what you write on it, either, just as long as I get an idea of how much money you make, okay?" She was so surprised that I didn't threaten to turn her into the police, and eventually, she did stop prostituting. But that wasn't the best part. About a year and a half later - she had been working at a Wendy's, if I recall, but still needed help covering food costs, childcare, and medical insurance - I got a phone call from her, and she proudly announced that I could shut off her food stamps.
I don't know if you remember me. I had a gun and you stopped me from hurting myself. My doctors say I am doing better. One of them works with the people you work for. He told me he could get a message to you.
I don't know what would have happened if you hadn't talked to me that day, but the doctors are helping me. I am getting better. They put me in a special school, and they say I am doing good. The doctors say that other people are getting taken like I was. I hope you can help them like you helped me.
"Well, I most definitely can do that! What happened?"
"I got me a real job! I'm now a legit massage therapist!"
She then went on to explain that, because I had treated her like a human being, she felt confident in herself and had gotten a scholarship to attend a tech school. It just filled my heart with joy knowing that I had any affect on that young woman's life so that she could, ever so gradually, realize her worth as a person. Probably one of my favorite moments from my life.
Mass Effect 2
|Conrad Verner in "A Troublemaker"|
Via Jean Luc on Fanpop
Mass Effect 3
|Attican Traverse: Krogan Team|
Via Mass Effect Wiki
"Anybody ... got something to eat?"I love you, Grunt.
< Day 14: Favorite Loyalty Mission Day 16: Favorite DLC >
* Gah, it is so hard to listen to Ereba's response when I deliver Char's final message. I was way more emotionally invested in these two characters than I probably should have been. When I heard his recording during this mission, I immediately said, "Oh, nooooooooo, not Char!"