Underused 1000-1900 PODs

   Byzantium doesn't have its 11th century decline - say Basil_II does his job and organises a reliable heir, even if he doesn't produce a child himself.  When the Seljuk Turks come calling in the mid century they will probably be sent packing and Byzantium stays the most powerful Christian state.  Probably no crusades or if they are they might be directed towards Iberia or N Africa and a strong empire, having beaten off the Turks might well expand from N Syria into the southern part and possibly even Palestine.  Egypt is almost certainly beyond their reach and whether they can hold all those territories would be another issue but it could make a hell of a difference to world history. 

  Alternatively it might go for reclaiming Sicily before the Normans drive the Saracens out in which case there is a good chance of further Orthodox/Catholic clashes and you might even see a crusade called against the empire.  This could do wonders for relations between the Papacy and the western [HRE] empire.

  Of course assuming that the Mongols still turn up a hell of a lot is likely to change then but its doubful that Anatolia would change from its predominantly Orthodox and Greek speaking demographics which is going to have some big impacts.

  Wouldn't this be before the OP conditions?  Whether you believe it occurred during Roman times or later during the Muslim conquest as there is IIRC a lot of debate over that.

   The Sassanids for whatever reason, possibly avoiding the long war with Byzantium, cutting their losses shorter, throwing up a military/political genius or whatever manage to defeat the Muslim incursions in the 7th century and recover.

  This would mean that other than by sea or by missionaries Islam doesn't get further east than Mesopotamia [AKA Iraq].  Central Asia might end up contested by Zoroastrianism, Buddhism and Christianity.  Going to be a much different world.

  Plus does this make Islam stronger in the west - because less efforts being sent against Iran - or weaker - because it lacks the resources of the east and the prestige of victory there?  You could see Islam overrunning much more of the Med and Europe or possibly failing to get into Egypt, in which case it could find its period as a political power being fairly short.  I.e. either Byzantium or Iran or possibly even an alliance of the two defeat the new upstart and reduce it to a minor player, possibly holding out in southern and central Arabia.

  In that case could Islam alter to be more a religion of traders and merchants and lose its strong emphasis on warfare and military conquest?  Possibly even being a fairly pacifist religion like Christianity and Buddhism started to be?

  There is actually a TL I read once that achieves this and more virtually as a bi-product of the Trent Crisis ending in war between Britain and the union.  This sees the north forced to sue for peace in the autumn of 1862.  As part of the negotiations delegates are called for from assorted neutral powers and the US ask for one from Prussia.  At this stage Prussia is in a constitutional crisis with the king and conservative elements contesting with a liberal parliament over the king's desire for big increases in military spending and greatly reducing the power of Parliament to restrain the army.  It was at the point when the king was even threatening to abdicate.  OTL Bismarck manages to negotiate a deal which gives the king and the conservatives the power he desires and the rest is OTL history.

  Here a frustrated king, given the request for a Prussian representative at the peace conference a frustrated king turns to the person currently with him, just returning from a short spell as ambassador in Paris, and basically says "you will do".  Hence a rather unhappy Bismarck suddenly finds himself reading up on the situation in the US as he prepares for a trip across the Atlantic.  The TL didn't go past the ending of the peace settlement in N America but the implication was that the Prussian king would probably resign and you have a markedly more liberal Prussia as a result.  Which would likely change a lot about future developments in Europe although I suspect you might well see Germany, or at least its northern parts unified in some way under Prussian leadership.