It was Thorondor who picked up Maedhros and Fingon from Thangorodrim, and also saved Fingolfin's dead body from being fed to Morgoth's wolves.
"When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared. For a time: while the Firstborn are in their power, and while the Secondborn are young." But dost thou not now remember Kementari, that thy thought sang not always alone? Did not thy thought and mine meet also, so that we took wing together like great birds that soar above the clouds? That also shall come to be by the heed of Iluvatar, and before the Children awake there shall go forth with wings like the wind the Eagles of the Lords of the West.'
"In the mountains the Eagles shall house, and hear the voices of those who call upon us. But in the forests shall walk the Shepherds of the Trees."
This section follows from Yavanna's concerns that Aule's dwarves will be permitted to harm her trees. Although it does not specifically mention Maiar by name, it does say "will summon spirits from afar". At this time, however, only Valar and Maiar occupied Ea, so the spirits must be Maiar. Morgoth's werewolves and vampires were also maiar, and in my opinion so were the early dragons. Also, in Morgoth's Ring, Tolkien attempts to explain the origin of orcs, and one of his explainations is that some of the early orcs were also Maiar.
The same argument can be used for talking trees. Broo-ra-room.
Dragons were probably also able to reproduce, as during the War of Wrath there were quite a few of them flying dragons (Ancalagon probably had a lovely time during the centuries).
To generalize, every Ainu who'd take the form of one of the Eruhíni, or an animal form, would be able to produce offspring : Melian is the definite example here, although Gothmog is mentioned as Morgoth's son in HOME as well.
Why did Tolkien abandon the idea of the Valar having children in the end, anyways?
That could be one reason they weren't allowed to reproduce, just as why the Elves were limited to only a reletively limited child rearing years, so their offspring wouldn't crowd out those of Men.
It seems wierd that he makes them married, but doesn't let them have children.
Oh, but they did have children. The Children of Illúvatar were their children, albeit not in the physical sense.
And the Dwarves were Aulë's children. Orcs, Dragons, Balrogs, Trolls, Wargs and what not, were Melkor's children.