For X-Plane 10 & 11 - EADT X737:
These are superb aircraft, all the more astonishing because they are freeware, and both versions (737-700 and 737-800) are available with several liveries, and come complete with highly detailed virtual cockpits:
EADT X737-700 & liveries
EADT X737-800 & liveries
The X-Plane 10 version is fitted with with the default X-Plane 10 FMC, but when installed under X-Plane 11 the considerably improved X-Plane 11 default FMC becomes available.
That said, $20 will buy you a copy of the X737 FMC UFMC by Javier Cortes which is a full navdata supported Boeing FMC designed specifically for the EADT X737-700/800 (note: X737FMC for the EADT not his other FMC product).
Why not try it out without the UFMC first of all, and then take it from there? The only items that for me are slightly disappointing are that the upper overhead panel and the trim panel at the rear of the lower pedestal are missing.
For X-Plane 11 - The ZIBO Mod for the Default X-Plane B737-800:
Introducing the Zibo Modified 737-800X!
This is utterly superb, and is right up there with the very best payware aircraft. It's simply unbelievable that someone has taken the default XP11 Boeing 737-800 and modified it to this incredibly immersive and realistic degree. Right from the start you know that you're in something rather special and esoteric.
The default XP11 737 is good our of the box, but the Zibo Mod transforms it into something else - nearly every switch and button works as it should, and the FMC has been totally refurbished into a fully featured Boeing 737-800 FMC with full functionality.
Is it like the PMDG or iFly? Well, actually, yes, it is so good that it is in this league of payware, yet it is for free (excluding the cost of X11).
What makes it so good? Well, it is accurate, flies beautifully and has full functionality, and on top of this a free FMOD sound modification is available for it (here) that gives it dynamic surround sound as well, plus you can find 100's of liveries for it at the X-Plane.Org site (search for default 737 and/or Zibo Mod).
It's not all difficult to install and setup this aircraft, but do read the instructions as these will guide you through making a copy of the default XP11 737-800, renaming your new copy to 737-800X, and then copying (and overwriting) the ZIBO Mod and FMOD sound files/folders into your new 737-800X folder - that's it!
The sole limiting factor for me is the absolute lack of ADF receivers in the aircraft, understandable insofar as the USA may be throwing NDB's out of the ballpark, but the rest of the world is still using them, and so this omission alone may curb where you chose to fly the default or Zibo Modified X-Plane 11 737-800.
OK, you can throw in the identifiers into the FMC, but what about old school navigation - should we throw those techniques out of the window too? I think not!