From New Scientist, here is a short article discussing five cases of small populations forced to relocate or plan to relocate due to sea level rise, caused by climate change.
It is a little anti-intuative to think that the 15-25 cm or so rise we have observed on average over the last hundred years could affect an island, even one whose highest point is only 2.4 metres above sea level, like the Maldives.
The relevant thing to remember is that it is not pure and simple submersion of existing land that is at work, rather it is erosion accelerated by both direct and indirect means. As waves lap generally higher on shores, they wash those shores away a little. But there are contributing factors to that erosion that act as feed backs as well. The loss of coral reefs as they are either destroyed by bleaching events or other causes removes important natural breakwaters that dampen the energy of incoming tides and waves. Salt intrusion can also kill vegetation that would otherwise be acting as an anchor for soils that now wash away more easily.
This is similar to the problems faced in some Alaskan communities, only in this case it is the absence of sea ice during stormy months and thawing permafrost that has accelerated the erosion process, in some spots to as fast as 30 metres per year!
I think it is pretty safe to say that we are already seeing real examples of real people forced to move due to climate disruption.