Short answer
Many minor signs have appeared: the coming and death of the Prophet ﷺ, the splitting of the moon, the conquest of Jerusalem, a great fire in the Hijaz, barefoot shepherds competing in tall buildings, and the spread of killing, ignorance and open sin. None of the ten major signs, such as the Dajjal, has happened yet.
Belief in the signs of the Hour reported in authentic texts is part of belief in the Last Day. Linking hadith to particular modern people or dates is speculation and should be avoided.
The four schools agree on this.
Explanation
The Prophet ﷺ himself. He said, "I and the Hour have been sent like these two," joining his index and middle fingers. His coming was the first sign. "The Hour has come near, and the moon has split" (54:1), and the Quran says "already there have come some of its indications" (47:18).
Six signs he listed. He told Awf ibn Malik to count six things before the Hour: his death, the conquest of Jerusalem, a deadly plague, wealth so plentiful that a man given a hundred dinars is still displeased, a trial entering every Arab home, and a truce with the Romans that they would break (Sahih al-Bukhari). Scholars said several of these came to pass in the early centuries of Islam, and many identified the plague with the plague of Amwas.
The fire of the Hijaz. He said the Hour will not come until a fire comes out of the land of the Hijaz that lights up the necks of camels in Busra. Al-Nawawi and other scholars of his time recorded a great volcanic fire near Madinah in the seventh century of the Hijra and took it as this sign.
Signs spread through history and today. Barefoot, destitute shepherds competing in tall buildings (Sahih Muslim). Knowledge taken away, ignorance spreading, wine drunk and zina open (Sahih al-Bukhari). Time seeming to pass quickly, deeds decreasing, miserliness spreading and killing increasing.
Still to come. The ten major signs, including the Dajjal, the descent of Isa, Ya'juj and Ma'juj and the sun rising from the west, have not happened. Be wary of videos that tie hadith to today's headlines. See the full list in Signs of the Day of Judgement and Is the Day of Judgement near?
The evidence
Quran, Surah Al-Qamar 54:1
بِسْمِ ٱللَّهِ ٱلرَّحْمَٰنِ ٱلرَّحِيمِ ٱقْتَرَبَتِ ٱلسَّاعَةُ وَٱنشَقَّ ٱلْقَمَرُ ﴿١﴾
The Hour has come near, and the moon has split [in two].
The splitting of the moon is an early sign.
Quran, Surah Muhammad 47:18
فَهَلْ يَنظُرُونَ إِلَّا ٱلسَّاعَةَ أَن تَأْتِيَهُم بَغْتَةًۭ ۖ فَقَدْ جَآءَ أَشْرَاطُهَا ۚ فَأَنَّىٰ لَهُمْ إِذَا جَآءَتْهُمْ ذِكْرَىٰهُمْ ﴿١٨﴾
Then do they await except that the Hour should come upon them unexpectedly? But already there have come [some of] its indications. Then what good to them, when it has come, will be their remembrance?
Some signs of the Hour had already come in the Prophet's ﷺ time.
Sahih al-Bukhari 6504
Sahih... بعثت أنا والساعة كهاتين ...
"I and the Hour have been sent like these two."
The Prophet's ﷺ coming is itself a sign.
Sahih al-Bukhari 3176
Sahih... اعدد ستا بين يدي الساعة موتي ثم فتح بيت المقدس ...
"Count six things before the Hour: my death, then the conquest of Jerusalem."
Lists six signs, several of which have happened.
Sahih al-Bukhari 7118
Sahih... لا تقوم الساعة حتى تخرج نار من أرض الحجاز ...
"The Hour will not come until a fire comes out of the land of the Hijaz."
A sign scholars recorded as having happened.
Sahih Muslim 8
Sahih... أن ترى الحفاة العراة العالة رعاء الشاء يتطاولون في البنيان ...
"That you see the barefoot, naked, destitute shepherds competing in tall buildings."
A sign widely seen today.
Where the ruling is recorded
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on the signs of the Hour. Affirms the major signs, such as the Dajjal, Ya'juj and Ma'juj and the sun rising from the west, as true.
- Sharh Sahih Muslim (al-Nawawi), Kitab al-Fitan, hadith of the fire of the Hijaz. Records the fire near Madinah in the author's time as this sign.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.