Note: By project I mean, the entire project, not just what you are working on, but also what other team mates are doing.
At Triggit we are building technology around how to buy digital media. What does this mean? It means a start-up with less then 20 people evaluates over 12 billion ad impressions, across hundreds of millions of user records, every day. Since we bid and buy these ads in in Real Time we get less then 100 milliseconds to leverage the data provided by the sellers (people like google), the data provided by our clients (advertisers), internal data, and 3rd party data to dynamically evaluate and bid on inventory. We look at about 150,000 queries per second with hundreds of different bidders. Because of latency restraints and load balancing issues we can't work in the cloud, which means we must coordinate this entire effort across four data centers on three continents.
We legitimately deal with big data - so much data that its not worth storing the vast majority of it. Hadoop sort of keeps up, Hbase breaks regularly and the guys at MapR are up to some pretty cool stuff.
Who said an online advertising start-up couldn't be interesting :) Check it out at triggit.com.
Asking people to describe the "complexity" of their product also seems to invite bragging about over-engineering - I could make my blog require 3 datastores and a message queue (this seems to be popular in some circles), and then post about how I'm solving complex problems and you should come work for me.
For what it's worth, I'd describe what I work on right now as quite complicated from a UI/UX and "number of inputs" standpoint, but quite simple technically - so I guess it falls somewhere in the middle in terms of "complexity?"
Just don't have enough time, money, or knowledge, and could do with some help actually!