They're not just in Sweden, but the bulk of them in a particular region of Sweden, namely around Uppland and Södermanland; the Mälaren valley area), the old heart of [Svealand](http://en.wikipedia.org/wiki/Swedes_(Germanic_tribe). Sigtuna Municipality alone has 150 - as compared to 50 in all of Norway and 250 in Denmark.

It's really the opposite of anything to do with paganism. The majority of runestones were raised by Christians. To give one example U124, a large but not untypical one in Stockholm. It has a prominent Christian cross on it, of a design similar to those seen on many others in Uppland. (The Ängby stone is thought to have been carved by the same individual, some time around the mid-late 11th century.

Runes were just an alphabet. Even if Christianity led to their replacement by the Latin alphabet (with the possible exception of Dalecarelian rules ^* ), they didn't really have a 'pagan' connotation, certainly not to these early Christians.

Regardless of whether Pagan or Christian, most of them are also rather formulaic memorials, reading "<name> raised this stone after <name>, his <relation>" (Or her relation, some were commissioned by wealthy women) There are also common variations on the theme like adding "<name> carved the runes" or if the person who died was a Viking it might mention where he died.

U1011 in the University Park of Uppsala is an funny and unusually boastful one: "Vigmund had the stone carved in memory of himself, the most skilled of men. God help the soul of captain Vigmund. Vigmund and Åfrid carved the memorial while he was alive." This is also a 11th century Christian stone, with a cross on it, and mentioning "God".

In southern Sweden the Eskilstunakista grave marker (looks like a tomb but was not, it was on top of the actual grave) came about at the same time, but still often used runes and the Urnes and Ringerike styles of the Viking Age. By the late 11th-early 12th century you have the Stavkorshäll (Stave-cross stone) marking graves - first just crosses (and sometimes runes, as in the depicted one) and later evolved into the "Liljesten" (lily stone), by which point they look more Medieval than Viking Age, I'd say. But neither of those things were nation-wide (much less Scandinavia-wide) trends either; they were significantly more common in some places than others.

Now, runestones are not gravestones. But they fit into the context of early Christian memorials.

Christianity also caught on later in Sweden than in Denmark and Norway, and later in Svealand than in Götaland (the south). Denmark and Norway were at least nominally Christened by the mid-11th century, if not the early 11th century. The temple at Uppsala (assuming it existed) was written about by Adam of Bremen around 1075 or so, the short-lived pagan restoration in Uppland by Blot-Sweyn occurred around 1080 (if it did occur). So it's been suggested that these runestones may have been making a statement on the arrival of Christianity to this last bastion of Paganism. Similarily, the significance of Sigtuna, more important at that time than prior or later (e.g. coins were minted there), may be due to it being a Christian outpost in Uppland at a time while nearby Uppsala (more significant than Sigtuna before and later) was still held by pagans.

(^* Whether this is a continuous tradition is unknown. Dalecarlia is almost unusual among regions inhabited in that age, in not really having any runestones. At most, two are known; out of which one hasn't been seen since the 1860s, and the other is a fragment recorded on stone that's not from the area)