What age group had the highest number of HIV positive cases in 2012?

From the data, the total number of cases for each age group is:

• 0-4 years: 41
• 5-9 years: 34
• 10-14 years: 47
• 15-19 years: 290
• 20-24 years: 665
• 25-29 years: 680
• 30-34 years: 590
• 35-39 years: 410
• 40-44 years: 270
• 45-49 years: 160
• 50-54 years: 90
• 55-59 years: 40
• 60 years above: 15

Comparing these totals, the highest number of cases is 680.

The age group corresponding to 680 cases is 25-29 years.

The age group with the highest number of HIV positive cases in 2012 is $\boxed{\text{25-29 years}}$.