T-sql Restablecer número de fila en cambio de campo

Si está en SQL Server 2012, puede usar LAG para comparar el valor con la fila anterior y puede usar SUM y OVER para registrar los cambios.

with C1 as
(
  select custno,
         moddate,
         who,
         lag(who) over(order by moddate) as lag_who
  from chr
),
C2 as
(
  select custno,
         moddate,
         who,
         sum(case when who = lag_who then 0 else 1 end) 
            over(order by moddate rows unbounded preceding) as change 
  from C1
)
select row_number() over(partition by change order by moddate) as RowID,
       custno,
       moddate,
       who
from C2

SQL Fiddle

Actualización:

Una versión para SQL Server 2005. Utiliza un CTE recursivo y una tabla temporal para el almacenamiento intermedio de los datos que necesita iterar.

create table #tmp
(
  id int primary key,
  custno int not null,
  moddate datetime not null,
  who varchar(10) not null
);

insert into #tmp(id, custno, moddate, who)
select row_number() over(order by moddate),
       custno,
       moddate,
       who
from chr;

with C as
(
  select 1 as rowid,
         T.id,
         T.custno,
         T.moddate,
         T.who,
         cast(null as varchar(10)) as lag_who
  from #tmp as T
  where T.id = 1
  union all
  select case when T.who = C.who then C.rowid + 1 else 1 end,
         T.id,
         T.custno,
         T.moddate,
         T.who,
         C.who
  from #tmp as T
    inner join C
      on T.id = C.id + 1
)
select rowid,
       custno,
       moddate,
       who
from C
option (maxrecursion 0);

drop table #tmp;

SQL Fiddle