This will be easiest with the data.table
package:
dt = data.table(df, key="Year")
dt[,Remove:=any(diff(Year) > 1),by=ID]
dt = dt[(!Remove)]
dt$Remove = NULL
ID Year Measurement
1: 1 2009 5.6
2: 1 2010 6.2
3: 1 2011 4.5
4: 2 2008 6.4
5: 2 2009 5.2
6: 4 2009 5.9
7: 4 2010 2.2
8: 4 2011 4.1
9: 4 2012 5.5