Pompeii is open year-round, and because it is an archaeological site rather than a resort, the season matters mainly in terms of crowd levels and temperature.
Spring (April–June) is the best time: the weather is warm but not oppressive, and the site is significantly less crowded than in high summer. The wildflowers growing between the ruins are an unexpected bonus in April–May.
July and August bring extreme heat and large crowds. The site has little shade — a large-brimmed hat, sunscreen, and at least two litres of water per person are essential. Morning visits (open at 9am) are cooler and less crowded; midday is brutal.
Autumn (September–October) is nearly as good as spring. The heat has eased and the summer crowds have thinned, but the days are long and warm enough for a comfortable visit.
Winter is quiet and can be pleasant: mild temperatures (10–15°C), almost no crowds, and good light for photography. Some secondary areas and houses may close for maintenance in the low season, but the main sights are open.
Avoid visiting on Italian public holidays and summer weekends if you can help it — the Circumvesuviana is packed and the site itself becomes very crowded.