First off, what are you trying to accomplish? And how are the queries being run?
If it is in the SQL engine you can look into Client Request Statement Caching. It can cache the recent queries that have been run (up to 31 lines, I believe). Gus did a presentation on it at the Revolution conference last year. You can download the presentation
here.
You can use the same technique to get some information about certain ABL clients' call stacks. This has to be configured in advance, i.e. before you need it. The database doesn't maintain any master list of queries in the database or in a flat file. You can also get similar information about ABL clients' call stacks on an ad hoc basis, assuming you have access to the system where they are running, with the proGetStack command. This will get you module names and line numbers, so you will need source access for this information to be meaningful.
Either way, the techniques above are just point-in-time sampling, and are not comprehensive. OpenEdge auditing would not help you, as you can audit record create, update, and delete events, but not reads. And even if you could audit reads you really wouldn't want to unless this was a test database where you didn't care about performance. If you think about it, read auditing would turn every database read into a read and a write, and your performance would be abysmal. Also there would be some cost involved, in terms of development, testing, performance tuning, and additional administration overhead. It would also chew through a lot of disk space.
You could maybe do something by writing database trigger code, but is it whatever you're trying to accomplish worth all that effort?