CREATE TABLE dbo.Duplicates_GD
	(Ident int NOT NULL IDENTITY (1, 1),
	MemIdNew int NOT NULL,
	MemIdOld int NOT NULL )  ON [PRIMARY]

CREATE TABLE dbo.Members_GD
	(MemID int NOT NULL,
	JoinDate datetime NULL,
	PaidDate datetime NULL)  ON [PRIMARY]

insert into Members_GD (MemID, JoinDate, PaidDate) values(1, '01-01-2013', '01-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(2, '02-01-2013', '02-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(3, '03-01-2013', '03-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(4, '04-01-2013', '04-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(5, '05-01-2013', '05-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(6, '06-01-2013', '06-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(7, '07-01-2013', '07-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(8, '08-01-2013', '08-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(9, '09-01-2013', '09-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(10, '10-01-2013', '10-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(11, '11-01-2013', '11-15-2013')
insert into Members_GD (MemID, JoinDate, PaidDate) values(12, '12-01-2013', '12-15-2013')

insert into Duplicates_GD (MemIdNew, MemIdOld) values (11,5)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(7,3)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(9,7)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(11,9)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(5,1)

insert into Duplicates_GD (MemIdNew, MemIdOld) values(6,4)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(10,8)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(10,6)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(8,2)
insert into Duplicates_GD (MemIdNew, MemIdOld) values(12,10)

select * from Duplicates_GD order by MemIdNew, MemIdOld
select * from Members_GD order by MemID

Select * from Members_GD

MemID	JoinDate	PaidDate
1	2013-01-01 	2013-11-15
2	2013-01-08	2013-12-15	

alter table dbo.Members_GD
add FamilyId int

declare @FamilyId int = 1
declare @Changed int = 0

update Members_GD
set @FamilyId = FamilyId = @FamilyId + (
		case 
			when @Changed = 0
				then 0
			else 1
			end
		)
	,@Changed = (
		case 
			when PaidDate is null
				then 0
			else 1
			end
		)

select MemId = min(MemId)
	,JoinDate = min(JoinDate)
	,PaidDate = max(PaidDate)
from Members_GD
group by FamilyId