Is there a performance difference between inc(i) and i := i + 1 in Delphi?

There is a huge difference if Overflow Checking is turned on. Basically Inc does not do overflow checking. Do as was suggested and use the disassembly window to see the difference when you have those compiler options turned on (it is different for each).

If those options are turned off, then there is no difference. Rule of thumb, use Inc when you don't care about a range checking failure (since you won't get an exception!).

It all depends on the type of i. In the Delphi programming language, one normally declares loop-variables as i: Integer, but it could as well be i: PChar which resolves to PAnsiChar on everything below Delphi 2009 and FPC (I'm guessing here), and to PWideChar on Delphi 2009 and Delphi.NET (also guessing).

Since Delphi 2009 can do pointer-math, Inc(i) can also be done on typed pointers (if they are defined with POINTER_MATH turned on).

For example:

type
  PSomeRecord = ^RSomeRecord;
  RSomeRecord = record
    Value1: Integer;
    Value2: Double;
  end;

var
  i: PSomeRecord; 

procedure Test;
begin
  Inc(i); // This line increases i with SizeOf(RSomeRecord) bytes, thanks to POINTER_MATH !
end;

As the other answers already said: It's relatively easy to see what the compiler made of your code by opening up the:

Views > Debug Windows > CPU Windows > Disassembly

Note, that compiler options like OPTIMIZATION, OVERFLOW_CHECKS and RANGE_CHECKS might influence the final result, so you should take care to have the settings according to your preference.

A tip on this: In every unit, $INCLUDE a file that steers the compiler options, this way, you won't loose settings when your .bdsproj or .dproj is somehow damaged. (Look at the source code of the JCL for a good example of this)