Is this plane going to be the biggest ever?
As a passenger jet, yes. Though Boeing’s 777 can seat 550.
There are bigger (650 seat) in development. Apparently Singapore Air has agreed to purchase already.
No. Define biggest, though. And, do you mean commercial passenger plane or any plane?
The Antonov 225 was (is?) bigger – 600,000 kg max takeoff weight (or 1.32 million pounds), vs. 1.235 million for the Airbus. See
http://www.xp-office.de/an225-technical.htm
vs.
http://www.airbus.com/product/a380_specifications.asp
The An 225 also had a wingspan of 88.4 meters, vs. 79.8 for the A380.
The A380 is up there, though. And it will be the biggest (in weight, passenger count, etc.) among commercial passenger aircraft – the An 225 is a military transport. It’s worth noting that the base 555 passenger configuration of the A380 is not that much bigger than previous max capacities – 747s can be configured to seat at least 509 passengers (which I know because JAL had one crash into a mountain in the deadliest single-plane accident ever).
Yes, the rub is what the definition of “biggest” is.
The Spruce Goose had a larger wingspan and was only 10 feet shorter than the A380. Which is bigger?
The A380 will be the largest “commercial passenger jet”. That definition eliminates the Spruce Goose (not a jet) and the An-225 (not a commercial airplane). The “biggest airplane” will always be subject to what you are measuring - wingspan, weight, etc.
Yeah, us airplane types are a little obsessive! 
And if youar talking internal volume then maybe the Airbus A300-600ST might be a contender http://www.airbus.com/media/a300_600st.asp
http://www.airbustransport.com
Brian
Well, the 555-seat capacity is for a “typical 3-class layout”… if you cram all economy seats in there (which, I believe is what you need to do to get the 550 capacity on the Boeing 777) I think the A380 capacity is something in the 800-900 range.