Bet you haven't seen this topic coming...

[Elmo]

According to the Silmarillion there are a few things that the Valar haven't forseen, things in each age that do not 'arise from the past' or some such thing I mistily recall. What are these events? I'm guessing the love between Beren and Luthien and maybe the attack on the lamps because they seemed completly unprepared for that, maybe the destruction of Numenor aswell.

[Feanorsdoom]

I'm right in the middle of Morgoth's Ring, so I'd say Miriel's death in Valinor, for one. It caused not only a big hullaballoo amongst the Valar, but forced JRRT to outline the rules for death and marriage for the Elves.

[Elmo]

Does this mean that if they haven't forseen these events, they can't forsee events that lead on from it? Like for example, couldn't forsee Miriels death therefore couldn't forsee Feanor's revolt or couldn't forsee destruction of Numenor so couldn't see creation of Gondor and Arnor. If that is true then there forseight isn't very impressive...

[Morwen]

Yet some things there are that they cannot see, neither alone nor taking counsel together; for to none but himself has Iluvatar revealed all that he has in store, and in every age there come forth things that are new and have no foretelling, for they don not proceed from the past.
Silmarillion, Ainulindale

Originally Posted by hewhoarisesinmight

Does this mean that if they haven't forseen these events, they can't forsee events that lead on from it? Like for example, couldn't forsee Miriels death therefore couldn't forsee Feanor's revolt or couldn't forsee destruction of Numenor so couldn't see creation of Gondor and Arnor. If that is true then there forseight isn't very impressive...

I don't think so. They might possibly foresee an event without necessarily having foreseen all the circumstances that lead up to it, i.e. seeing individual links in the chain but not the chain as a whole. It could be that their foresight provides them with a fair idea of the "big picture" but doesn't necessarily, in every circumstance, allow them to foresee exact details.

Of course on the point of foresight, Mandos should probably be distinguished from his brethren as he "knows all things that shall be, save only those that lie still in the freedom of Iluvatar" (Silm., Valaquenta) I guess in answering the question of what are the things that the Valar can't foresee, a useful starting point is determining what things take Mandos by surprise/seem outside his knowledge. I think that the Beren/Luthien situation that you cite is a good example of this. Earendil's fate (and that of Elwing and their sons) may be another.

[Legate of Amon Lanc]

I think the main point was in the "freedom of Ilúvatar", meaning simply that there are some things that are lined, you know, "logically" and for Valar (maybe even from some Wise among Elves or Men) they can be expected from what happens before. You know, something like it is logical that if A leads to B, then when A happens in the history, we will expect B to happen (of course, this is just a very simple scheme, the knowledge of Valar is of course transcending the simple logic of Elves or Men, but they probably also have some sort of "logic"). But there are things that are totally unexpected and can emerge "against logic", because they come from Eru's freedom. For example, I think the most obvious event like this is the emergence of hobbits.

[Raynor]

Originally Posted by Morwen

determining what things take Mandos by surprise/seem outside his knowledge

It seems that the limits of their foreknowledge is their memory of Ainulindale:

Originally Posted by Letter #200

Knowledge of the Story as it was when composed, before realization, gave them their measure of fore-knowledge; the amount varied very much, from the fairly complete knowledge of the mind of the Creator in this matter possessed by Manwe, the 'Elder King', to that of lesser spirits who might have been interested only in some subsidiary matter (such as trees or birds).

[Morwen]

Originally Posted by Raynor

It seems that the limits of their foreknowledge is their memory of Ainulindale:

I agree and would add as a limitation their limited viewing of the vision of the Ainulindale as made visible to them by Eru :

.... and while the Ainur were yet gazing upon this vision, it was taken away and hidden from their sight; .....for the history was incomplete and the circles of time not full-wrought when the vision was taken away. And some have said that the vision ceased ere the fulfilment of the Dominion of Men and the fading of the Firstborn; wherefore, though the Music is over all, the Valar have not seen as with sight the Later Ages or the ending the World.
Silm., Ainulindale

The ability of the Valar to foresee events in the Fourth Age and beyond is restricted, especially as these ages are dominated by Men who have the power to shape their lives beyond the Music of the Ainur.