Simon & Garfunkel once said, "Everything looks worse in black and white."
The song was "Kodachrome", a tune that probably every photographer is familiar with.  Paul and Art changed "worse" to "better" during their 1981 concert in Central Park.  No doubt a nod to their advancing age.
Or they just forgot the words.  Hard to tell.
Anyway, the decision to apply a monochrome ("black and white") treatment to a photo depends on many things. Probably the most important, I think, is the color, textures, and contrast in the image.  Some images pop in monochrome, some don't.
Also important is the mood of the photo - or at least the mood that you're going for.  A great variation on the standard monochrome treatment is "sepia" toning (pronounced "see-pee-ya", though maybe not in mixed company).  An image rendered with sepia toning has more of a reddish-brown coloring, and generally has the feel of an old photo, or at least a photo of an old subject. 
So, if that's the mood you'd like to achieve, sepia will help get you there.
I applied a sepia treatment to several interior photos taken while visiting Casa Loma, a Gothic Revival mansion in Toronto.
Sometimes, a monochrome/sepia treatment helps a photo, sometimes it doesn't.  I'll share both the color and the sepia images here, and let you decide.
Image 1 – An Old-Timey Telephone
Let's start simple, with this image of an old-style telephone, nestled in a nook in the wall near one of the larger rooms of the mansion.
Here’s the color image:

And here's the sepia image:
You be the judge - which is the better treatment?  Is the color image more pleasing to the eye?  Or, does the sepia image add a historic feel to the photo? 
My opinion?  I like the sepia version.  It works especially well for this subject, for obvious reasons.  By the looks of it, that photo could date back to the early twentieth century. (It actually came from the early twenty-first century.)

Image 2 – Sir Henry’s Suite
Before we go on, you may be wondering, “Why is it called sepia?”
You may not have been wondering that, but work with me here.
According to Wikipedia, the reddish-brown color known as sepia is named for the brown pigment derived from the ink sac of the Sepia cuttlefish.
Interesting, eh?
Actually, it's kind of disgusting - the definition, I mean.  The actual fish is even more disgusting - Google it and you'll see what I mean.
Anyway, a sepia treatment can add character to a photo that would otherwise be lacking.
In the next image, also from Casa Loma, we see a bedroom - called "Sir Henry's Suite", referring to Sir Henry Pellatt, the Canadian financier and soldier for which the house was built.  You be the judge - is the image better in color?:
Or is the image better with sepia toning?:
I prefer the sepia version again here.  In this case, this is not a great photograph.  It could be focused better, and I couldn't remove all the noise (graininess).  I took the shot quickly while crouching down, in low light, with an iPhone.  But I thought it was good enough to illustrate this point since the grainy and slightly unfocused aspects make it look genuinely old when rendered in sepia. 
That’s really just my way of rationalizing the use of a bad photo.  But bear with me.  The point is that a sepia treatment can save an image that might otherwise be lacking.

Image 3 – The Conservatory
So far, we've seen a couple of photos that, in my humble opinion, clearly look better with a sepia treatment.  Now I present to you a photo that (spoiler alert) may go the other way.
This image, like the others, is from Casa Loma in Toronto.  It's the conservatory, a room filled with natural light and plant life.  The image is a small panorama.
Here's the color photo:
And here's the photo with a sepia treatment:
No doubt the sepia photo, like all sepia-toned images, has an aged feel to it, and that lends it a certain cool factor.  It looks like a movie scene from the 1920s.
But in this case, unlike the others, I think this image is better in color.  The full-color image allows you to "feel" the warm sunlight coming through the windows.  And natural plant life always looks better in vivid color, as does the stained-glass dome.
But you be the judge. 

So, What Is Sepia Actually Good For?
"Absolutely NOTHING" might be your knee-jerk response to that question, if you know the song. 
But if you’ve read this far, you know the real answer.  A sepia treatment adds character and mood to a photograph, often making it look older than it is.  Even if the viewer knows that the effect was added with software, that old-timey mood is still there.
At a time when photos are expected to be high-resolution with tack sharpness and hyper-accurate color, it’s often comforting and enjoyable to create images that simulate the look of yesteryear. 
Even if it takes the coloring of a disgusting cuttlefish to do it.
Comments or questions?
Let me know below.
Thank you!