Here are my PC market share numbers for Q3 2010, which, as always, are based on averaging the numbers provided by both IDC and Gartner. Why? Because both firms measure things a bit differently.
Top 5, US market
1. HP - 4.5 million units
2. Dell - 4.3 million units
3. (Tie) Acer/Apple - 1.9 million units
4. Toshiba - 1.6 million units
Total: 18.24 million units (revised: I originally had mistakenly put 26 million units here)
So, as you can see, while IDC had Apple coming in third place, and Gartner had Acer in third, when you average the numbers, you actually get a tie. It should be noted that Apple is on the way up, however, and Acer is flat or down slightly. So the "third place" claims for Apple are pretty reasonable. (If largely non-researched.)
Top 5, worldwide
1. HP - 15.6 million units
2. Acer - 11.6 million units
3. Dell - 11 million units
4. Lenovo - 9.2 million units
5. ASUS - 4.8 million units
Total: 91.5 million units
We can't calculate Apple's worldwide market share until the company releases its actual quarterly sales figures. I will do so at that time, but based on the numbers above, Apple owns ~10 percent of the US market (and not 10+ percent as as widely reported).
Update: Math is hard. I made a calculation mistake in the original version of this post and have corrected it. My bad. --Paul