Does your engine produce the design power.

[Biggles]

What is to say my engine is sick? Down on power and in imminent danger of failure?

I am thinking along the lines of carbon build-up, worn jets, and such like. EGTs are the obvious one but not all aircraft have them.

[Mogas]

A very good point Biggles.
There are many engines in service that just do not deliver what it said on the tin when they were new.
It is important to understand that performance figures quoted in the POH are for a new engine and propeller.
As you mentioned, carbon build-up, carb wear & tear as well as worn rings, nicks and scrapes on the prop, blades not tracking perfectly and so on all come together to significantly reduce engine performance.
Then when one also factors in density altitudes and humidity (ISA assumes dry air) it becomes quite obvious why pilots sometimes get caught out when they thought they had more performance available for that hot, high, humid and heavy takeoff.
One of the most basic and best checks is to ensure you get the advertised static RPM on the pre-takeoff engine run-up. This is often not practical due to dirt runways and so on but this check is just as relevant on the early take-off roll, even if the aircraft is not quite static, it takes quite a lot of forward speed fot the propeller to fully "unload".
This check is unlikely to point to an imminent failure as such but will show up a motor and/or prop in need of some detailed attention.
Mogas

[Boet]

2-stroke engines are very clear about this: If something is not the way it is supposed to be, the engine is trying to tell you something! Heed it`s warning call!!

[Jean Crous]

2-stroke engines are very clear about this: If something is not the way it is supposed to be, the engine is trying to tell you something! Heed it`s warning call!!

Yes , otherwise a steady ggggghhhhhllllliiiiimmmmmmm may change into ......GGGGGGLLLLLaaaaaallllllaaaaBBBaaaBBaaaaa...silence

[Dobbs]

If your engine was correctly set up in terms of the prop when new, and the prop is still in good condition and the engine is still developing the correct rpm at take off, then, assuming you have a fixed pitch prop, your engine is still developing its rated horse power.