What is the best Scheme interpreter or compiler?

I'd recommend not being concerned about whether it's implemented as a compiler, interpreter, or combination thereof -- especially to start with, the quality of help files (for one example) will matter far more than exactly how it's implemented.

As far as which one, DrRacket is what I use (by far) the most often.

For a beginner, I would highly recommend DrRacket (formerly Dr. Scheme), since it gives you a really nice environment to work in, supports many dialects of Scheme, and gives very good failure and debugging information. I believe most implementations of Scheme are interpreters, although it is possible that there is a compiler out there.

If you are a commandline junkie like me, an alternative you might consider is to run the racket interpreter directly, which is essentially the same thing as Dr. Racket, but without the graphical environment and a commandline interface. Or, start your source file with #! /usr/bin/env racket and make it executable with chmod +x source.rkt.

I'd recommend Gambit-C scheme:

• It's R5RS-conformant.
• It has both an interpreter and a compiler. You can also compile to ANSI C.
• It's open source.
• It's portable. (It runs on Linux, Windows, Mac OS X and even iOS.)
• It has simple foreign function interfaces (FFI).

A cursory examination reveals that Chicken seems unsatisfactory, while Bigloo may be a serious contender. But I cannot comment too much about them.

I know you already accepted the answer, but for future visitors to this question, I recommend Chicken Scheme. It tends to produce much smaller executables than mzscheme does. Take the following hello world application, for instance:

(define (say-hello name)
  (print (string-append "Hello, " name))
  (newline))

(say-hello "Earthling")

Compiled with mzc --exec mztest hello.scm: 3.3M

Compiled with csc hello.scm -o ctest: 16k

And if you're after library support, Chicken provides Eggs Unlimited, which is like PlaneT for mzscheme (or gems for ruby).