How much is a safe minimum layover time?

There is no general answer. It depends on many factors:

• how far you physically have to travel between leaving one plane and boarding the other. I have had this be as little as two minutes (nearby gates in the same terminal) or over 30 (go to another terminal via bus - oh LAX, I hate you so much)
• do you need to clear immigration and customs to enter the transit country, either because it's your "first port of entry" or because they don't have airside transit (here I am hating LAX again), anyway add up to an hour for this, since in addition to lining up and speaking to an officer you probably also have to wait for luggage and hand transfer it somewhere else
• do you have any kind of status with the airline (people with status don't generally ask, but anyway such people may be met by golf-cart-driving airline staff, and/or the departing plane may be held for them)
• how likely is your incoming flight to be late (a good opportunity to hate ORD arises here)
• is there another flight shortly afterwards that you could easily be put on if the connection is busted?

I have made connections when the incoming plane landed after the outgoing plane started boarding. I have also run through FRA, desperately begging people to let me go to the front of lines, and needed a full hour to only just make that connection. (In contrast a 1 hour connection in MUC will give you 20 minutes to kill at the gate, and you will never have butted into a line or run.) In some large airports even two hours is not a generous connection time if you have customs and immigration to deal with.

Generally the airline establishes a minimum connection time and won't sell you anything tighter. If you're not sure whether to book something that tight, take a look at their recommended times for arriving at the airport for locals. If you're supposed to get to the airport two hours before a flight, yet your incoming flight is getting there 61 minutes before the outgoing leaves, that's a little worrying, unless there's an airside transfer process and you know your bags will be checked straight through. On the other hand if they say to arrive 45 minutes before the flight, your same 61 minute connection will probably be fine.

There are quite a few questions here of the form "is x minutes enough time for a [domestic/international/Schengen-nonSchengen] transfer at [airport name or code]?" I suggest searching for some to gain information about the particular airport you're considering.

Airlines publish a minimum connection time various combinations of airport, terminals and flights. Now I feel that many time it is unrealistic and have been caught by such connections several times, despite doing my best effort to meet the connection. It has happened that my luggage has missed the flight but I managed and vice-versa.

The Dubai airport is particularly large and there are some terminal changes where you have to lineup for passport control which can cost you 20-40 minutes depending how busy it is. Since your example are two international flights, you do not have to pass immigration though and your luggage should be transferred without your intervention. This helps but sometimes they do not notice the tight schedule and the luggage is not transferred on time. Last time I was flying out of Dubai with a 45 minute layover in Bangkok on the way to Hanoi, I mentioned it at the check-in counter and they tagged my luggage with a bright yellow sticker that said "Hot Transfer". It made it and so did I, only just. The gate closed less than 5 minutes after I boarded.

Usually with 90 minutes layover time, unless there was a flight delay, I have never missed any flight. For domestic connection, I usually consider 1 hour enough. As someone said in the comments, if you do miss the a flight, the airline has to accommodate you on another flight but it can be quite a pain and cause other issues such as loss of hotel, missing another flight, boat, train, etc.