How close are we to the end times?

To give a quick reply, in Jesus' Olivet Discourse (Mt. 24-25) he gives the "signs" that will foretell the end of times. To summarize:

1. Many false claimants to be the Messiah will come.
2. Global instability (Wars and rumors of wars)
3. Famines
4. Earthquakes.
5. Great persecution of Christ-followers.
6. Increasing wickedness causing "the love of most to grow cold." (seems to be referring to the love of God.)
7. Global preaching of the gospel (leaving no one without an excuse)
8. Desecration of the Jewish Temple. The "Abomination of Desolation" refers to a desecration of the Temple like that of Antiochus IV of Syria (165 BC) who sacrificed a pig on the altar of the Jewish Temple and dedicated the Temple to the pagan god Zeus. The AntiChrist is being foretold as one who will do something even worse. Obviously, this prophecy requires a rebuilding of the Jewish Temple in Jerusalem which has not yet happened.
9. Great distress.
10. False prophets will perform many signs and miracles.
11. The final sign is disturbance in the skies. Sun darkened...moon as blood...stars fall from sky. These are phenomenological descriptions (what is seen is being described, not what has happened.) In other words, something like a nuclear holocaust will cause dramatic effects in the perceived sky. Jesus is using the language of the day to describe these cataclysms.

Jesus follows up this list with the following instruction:

32"Now learn this lesson from the fig tree: As soon as its twigs get tender and its leaves come out, you know that summer is near. 33Even so, when you see all these things, you know that it is near, right at the door. 34I tell you the truth, this generation will certainly not pass away until all these things have happened. 35Heaven and earth will pass away, but my words will never pass away.

Here is our time marker...the generation which sees these signs will not pass away before the completion of events. In other words, once the Temple is erected, these events will take place within the lifespan of a man. A generation can be reckoned in a variety of ways. The generation under judgment in the wilderness was 40 years. The generation of captivity in Babylon was 70 years. The upper maximum of a man's life is fixed now at 120 years (Gen. 6).

Back to your question. How close are we? We already see indications of most of these signs. Certainly we see great political instability in the world. We see many global disasters, both natural disasters and famines. Wars and rumors of wars abound. Radicalized Islam has certainly contributed to this global instability. There are several signs which have not taken place. However, the plate is set and these signs could progress rapidly.

The two limits that I see are the lack of a Jewish Temple and the failure to complete the message of preaching the gospel to all people. There are still many unreached people groups, although the work of Bible translation and missions work is moving forward. Computer technology has propelled this process. There are ongoing Temple excavations. Zionists in Israel are highly motivated to see the Temple rise, not so much as a religious institution, but a national symbol. This may explain how the AntiChrist will make quick inroads into the Temple, if it is largely a secular cathedral. I would say when we see that Temple rise, start counting.

Jesus does give us a warning near the end of Matthew 24:

36"No one knows about that day or hour, not even the angels in heaven, nor the Son,[f] but only the Father. 37As it was in the days of Noah, so it will be at the coming of the Son of Man. 38For in the days before the flood, people were eating and drinking, marrying and giving in marriage, up to the day Noah entered the ark; 39and they knew nothing about what would happen until the flood came and took them all away. That is how it will be at the coming of the Son of Man. 40Two men will be in the field; one will be taken and the other left. 41Two women will be grinding with a hand mill; one will be taken and the other left.
42"Therefore keep watch, because you do not know on what day your Lord will come. 43But understand this: If the owner of the house had known at what time of night the thief was coming, he would have kept watch and would not have let his house be broken into. 44So you also must be ready, because the Son of Man will come at an hour when you do not expect him.
Jesus warns us not to be too precise in our attempt to date these events. Yet, at the same time, the apostle Paul warns us not to be clueless. In 1 Thessalonians 5 Paul seems to contradict Jesus:

1Now, brothers, about times and dates we do not need to write to you, 2for you know very well that the day of the Lord will come like a thief in the night. 3While people are saying, "Peace and safety," destruction will come on them suddenly, as labor pains on a pregnant woman, and they will not escape. 4But you, brothers, are not in darkness so that this day should surprise you like a thief.
I don't believe that this is a contradiction, but rather the other side of a continuum. Jesus speaks of a thief in the sense that the events will go zero to sixty...there will be a quick escalation of these signs of the times as they start to unfurl. Paul is addressing Christ-followers and reminds us that Jesus has given us signs to interpret the times. We should not be clueless in discerning these signs.

I'll give you one other marker to look for. The book of Revelation describes 144,000 Jews for Jesus, 12,000 from each tribe. As of yet, the modern State of Israel has not subdivided itself into territorial districts. However, it makes sense that at some point they will do so. It also makes sense that when they do, they will "resurrect" the old tribal names. When you see a modern map of Israel with names like Asher, Naphtali, Levi, Judah, Reuben, Simeon, etc., we are inching closer to these events.

Bottom Line: We are getting close, but not yet. Keep looking on the evening news...the signs will be obvious.