I have an 8 night booking at an Australian hotel (Hilton Cairns). If I book each night individually I'll save an average of AUD60 per night off the best rate. It's very tempting though there is also the strong chance that they will make me change rooms or stand me at the front desk while they link them.
I should also say that HH has never got correct multi-night bookings for me and it has always required a phone call or an email and a copy of the bill to sort it out.