Some of these examples might not fit into a timeframe of possibilities. But perhaps an equally great journey over long distances occurred, and if so how common was it?
Yes, this is quite possible. You might possibly be known in Sarkland as 'the Icelander' because of your rarity, and if you would make it back home you would be known by future generations as 'the Far-Travelled'. The Icelandic sagas that actually deal with figures who did this, such as Ingvar, deal exclusively with Christian characters, though, and being Christian (and being able to navigate through the Rus/Byzantine hierarchies and social structures) would definitely be a benefit. This is why the sagas that refer such characters take place slightly later, between ca. 980 and 1050. However, we should not read the sagas too literally (they after all also represent Christian pilgrimages from the period in which they were written down, the 13th/14th/15th centuries), but rather use them as indication of what might have been conceived as plausible to their intended audience. This means that their narratives are on the one hand believable enough to maintain suspension of disbelief, but on the other hand remarkable enough to maintain interest. An Icelandic Viking in Baghdad would definitely fit that range.
Well, Harald Hardrada (d. 1066) was born in Norway, travelled to Sweden and Kiev before spending several years in Byzantium as a mercenary in the Varangian guard where he travelled a fair bit, to the Holy Land (maybe), to Syria, Armenia, and to Sicily. So not quite Iceland to Baghdad, but a pretty good journey.
My source is 1066 The Year of the Three Battles by Frank McLynn.