Whitney has asked this question and I’m going to try and answer it.
In order to answer this question it first becomes necessary to understand the meaning of the term ‘technology’. Answers.com has two definitions, given below:
1. The application of science, especially to industrial or commercial objectives.
2. The scientific method and material used to achieve a commercial or industrial objective.
By these definitions, therefore, technology started around the time humans began to engage in commerce, or the exchange of goods and services.
But let’s pause and look at the first definition again. Technology is, primarily, the application of science. Just because it is especially related to industrial or commercial objectives does not imply that that is its ONLY purpose.
When we accept that technology is the application of science, we realise that technology probably started around the time the first caveman picked up a rock and brained the neighbour who was hitting on his wife. Well, Mr. Caveman then realised that the rock made a handy weapon and probably then used it to bring down his next prey.
Of course, I was being a bit facetious, but I think it stands to reason that technology thus started the minute a tool was used.
And this brings us to another astounding thought: Technology is not limited to humans!
Apes use tools. So do crows and some other birds.
Technology, then, in my opinion, started the minute the first creature picked up a blade of grass and used it to pick ants out of an anthill.
For more in-depth analyses of modern (as in the last 1000 years or so) you can take a look at the following sites:
Institute for the History of Technology and Industrial Archeology
History of Technology Research Unit
Wikipedia's resources on the History of Technology (goes back to prehistoric times)
About.com's History of Invention and Technology Timelines