A few, in some degree

The parliamentary committee which oversees the process issued a report in November covering the first year. They identified a few success cases:

Sugar tax - petition initially dismissed, but rolled into a larger ongoing debate around the topic; the government later announced such a tax would be brought in from 2018.

Meningitis B vaccination - after committee enquiry government agreed to provide a new public health campaign on meningitis symptoms, and to review how funding for vaccines is allocated.

Brain tumour research funding - petition prompted an enquiry, after which the government conceded the need for increased funding. This is now under review - The Government agree that a greater level of brain tumour research is urgently needed [...] the Minister for Life Sciences will be convening a working group of clinicians, charities and officials to discuss how working together with our research funding partners, we can address the need for more brain tumour research.

So that's one success (where other campaigns, not just the petition, also contributed); one probable success but still being worked on; and one related positive change albeit not quite the thing asked for.

As none of these were apparently the "most shared" petitions in 2016 (for a start, one was in 2015), they won't have been picked up by the New Statesman article quoted in the other answer.

The review noted a fourth enquiry, the petition on high heels and sexism in workplace dress codes, but at the time of writing there was not an identifiable outcome from this. However, just last week the committee issued their report:

The government has said that the existing law is clear, and that the dress code that prompted this petition is already unlawful. Nevertheless, discriminatory dress codes remain widespread. It is therefore clear that the existing law is not yet fully effective in protecting employees from discrimination at work. We call on the government to review this area of the law.

So if this progresses further, there will be a fourth case to point to. Whether it will, good question, but IME it seems likely.

One thing to bear in mind here is the timescales. Two of the four examples here are on the way to a positive change that does what the petition wants, but are taking time to get there. And since we've only had a petition system since mid-2015, there won't be many done-and-dusted cases...