What if Harald Hardrada wins the throne of England?

  It might depend on how long he stays and how strong or not he is after defeating William.  Hardrada was more of a looter than a ruler from what I understand it and if he took considerable losses defeating William after 1st defeating Harold there might not be enough forces left to do more and extort a lot of money from the English and then return home.  Especially since a weakened king absent from his homeland could see Swain of Denmark make a move against Norway in revenge for all of Harald's attacks on Denmark.

  Of course if the PoD is that William isn't delayed in invading and is defeated by Harold, who is then weakened enough that he's defeated by Harald that could be a different matter.  In that case England could be under foreign rule for a period but its not likely to be lasting.

  Either way England will have a difficult period with probably some internal fighting even if they 1st have to drive out the Norwegians but its unlikely to be as savage as the Norman occupation and a lot more of English culture will survive.  Definitely more links with Scandinavia and probably also N Germany and associated regions.

  Of course no Norman conquest and probably the death or at least a serious defeat for William would reduce Norman power in France somewhat as well which could mean either an earlier strengthening of the French monarchy or another regional lord or combination of challenges the dynasty.  Which could have all sorts of impacts and neighbouring regions.  Especially since, baring the Byzantine empire sorting itself out and not losing most of Anatolia and other eastern areas, your likely to have the crusades starting.