It's been confirmed. Although the details about how psychic powers are going to work in the new edition are still unknown, it is now clear that anyone can summon Daemons. Specifically...
the Primaris power allows you to summon one of the following:
10 Bloodletters
10 Pink Horrors
10 Plaguebearers
10 Daemonettes
5 Flesh Hounds
3 Flamers
3 Nurgling Swarms
3 Seekers
Additionally, with a different power, you can summon one of the following:
3 Bloodcrushers
3 Screamers
3 Plague Drones
3 Fiends
Note that the conjured unit will appear within 12'' of the psyker. Conjuration powers are new, and it is not yet known exactly how the unit will enter the table (merely placed? as per Deep Strike?) or what limitations will be placed on their actions on that turn (will they be able to act normally? will arriving count as their movement, but they can still shoot and assault? will they be treated as entering from Reserves and be unable to assault?). When that information is released, it may alter our findings, but I see no reason we can't begin discussing now.
Here's the question as I see it: in most cases, those of us who aren't primarily Daemons players aren't going to want to buy one of each. We are probably going to want to get one - maybe two - top choices. The right Daemons for our army.
The question is, which Daemon is that?
The following armies (all armies with psykers who are not Tyranids) can summon Daemons:
Astra Miliatrum
Blood Angels
Chaos Space Marines
Dark Angels
Eldar
Grey Knights
Orks
Space Marines
Space Wolves
Let's have a lively discussion. When some kind of consensus is reached, I will modify the OP with a summary of our findings and a brief explanation of the logic that led to that recommendation.