According to this source (which seems consistent with other sources such as PC Gamer and IGN), this is the list of characters with whom you can romance.
Edit: Added some known commitment requirements for certain NPCs.
- Cora (Scott Ryder) - Commitment required.
- Liam (Sara Ryder) - No commitment.
- Peebee (Scott or Sara Ryder) - Commitment optional.
- Jaal (Sara Ryder) - Commitment required.
- Vetra (Scott or Sara Ryder) - Commitment required.
- Gil (Scott Ryder)
- Suvi (Sara Ryder)
- Reyes Vidal (Scott or Sara Ryder)
- Keri T'Vessa (Scott or Sara Ryder) - No commitment.
- Avela Kjar (Scott Ryder)
- You can flirt with Lexi T'Perro but they shut down either Ryder.
- Some crew members have flirtatious interactions with other crew
Tips from the IGN guide:
"The way to romance characters is rather standard: flirt when you see
the heart icon, and if the character is interested, they'll convey
that to your chosen Ryder. Most will update their conversations after
you complete a major mission or character specific mission that'll
allow you to further your romance.
Flirting with every character at the beginning doesn't hurt your
chances with the others later on."
Also noted about the romance system by the producer:
"Ryder's personality is slowly set by those tones, with new
conversation options and character interactions unlocking when he or
she reaches different thresholds within those personality types."