AFAIK the various 'invasions' of Angle-land were triggered by the geo-political situation of the time (the rise of the Godwinsons, the death of Edward the Confessor, political marriages and off-spring etc.) all of which triggered great interest in the 'English' throne. Read "The Norman Conquest" by Marc Morris for an informed and detailed description of the events leading up to the battle of Hastings, and how William's dreams for a united Anglo-Norman realm were then dashed within a few years.
To Draccan's question about the Normans invading Denmark or the Vikings invading Great Britain, don't forget that the Danish Vikings ruled a significant part of 'Scotland' from the 8th to 13th centuries and the Orkneys and Shetland were only transferred to Scottish rule in the 15th century. But for the intervening Kingdom of Scotland ruled by King Malcolm (who defeated MacBeth - yes that one), the Normans might have conceivably fought the Vikings on 'British' soil. However the politics and especially the distances involved made that physically impossible - but a nice 'what if' scenario.
Stretching the imagination *much* further, it seems that the Normans of this period were almost entirely motivated by gaining land / territory - whether in conquering Normandy and Northern France, England, Italy and Sicily or the subsequent Crusades and the Outremer states of Edessa and Antioch. So Deccan asks 'What if' William raised an army to invade Norway under the plausible counter-claim to the throne of Harald Hardrada, or even the throne of Denmark (which Harald had unsuccessfully tried to claim in 1064)? The 'Normans' were after all essentially Vikings themselves, whose Leader (Rollo) was allowed to settle in northern France by the Carolingan King Charles the simple.
To do this, William would have made promises of territory to those that supported him and they would have been expected to provide arms and transport etc. (which was what he did to mount the 'Norman conquest'). Assuming he could rally enough willing nobles to his cause, they would then have sailed along the coast of northern Europe stopping at various ports etc to pick up supplies (or raiding if necessary) until they got to the intended destination. This advance would be widely known to the opponents, though the timing would be dependant on the weather and especially the winds. And yes, the boats would have been the same. Again, a nice 'What-if'.
Other 'What if' scenarios are much less likely, not least because the Norman invasion of Italy was one of the events that triggered the Crusades, encouraging European leaders like Frederick Barbarossa to go south rather than north. Equally the Moors were much more interested in nearby southern France / Europe rather than distant (and cold
) Britain.
This period makes for *very* interesting campaigns because of the numerous factors involved both political and logistical. There were claims and counter-claims to geographical areas, political marriages and murders were rife. Combats were usually skirmishes - pitched battles were very rare, not least because of the far reaching consequences of losing. And on top of this, the Church was also going though 'interesting times'.
Finally, in this period leaders were only as powerfull as the nobles or factions they could rally / bribe to support their cause. This was ultimately one of the main reasons for the subsequent problems experienced by William; the isolated Norman nobles were often unable to subdue the local populations of the 'fiefs' they had gained through supporting the conquest. As a whole, Norman nobles were also usually reluctant to risk what they had gained, so would only help their leader if it was in their interest to do so, whether it was William or the various Crusades.
Indeed King Harold suffered similar problems; his nobles had stationed troops along the south coast all summer and Harold only disbanded them when the invasion season was 'over'. But within one or two weeks Harald Hardrada had invaded near the Humber forcing Harold to race north gathering what troops he could. He released these from their duties after the Battle of Stamford Bridge only to be told of William's arrival in the south. Racing back south, Harold was again unable to raise sufficient troops to beat William in a full battle, so tried to catch William by surprise like he did the Vikings - but this time the strategy failed 'and the rest is history' as they say.
