I'm married and a married guy at wok wrote me a poem. Does he like me?

Obviously he more than likes you. No guy writes a women a poem that isn't at least a little infatuated.  Or maybe he is obsessed with Dana Scully.

What was the poem?

Roses are red, violets are blue,
I wrote this to say
that I hate you too. 

Just because I wrote you a poem doesn't mean I like you. 

Maybe. Or maybe he just sees you as a friend. It's hard to tell. But if you're married and he's married, then I guess it's a friend to friend gesture.

If the content of the poem is to cheer you up, then it is probably just that - he figured the poem might cheer you up.

He is obviously aware of your mood, which would mean he see you as a person, not just another face in the crowd. 

It’s too early to say there is anything more than a friendly gesture from him.

Yes he probably likes you.

Fleeting Perch
O nightingale! thou surely art
A creature of a "fiery heart":—
These notes of thine—they pierce and pierce;
Tumultuous harmony and fierce!
Thou sing'st as if the God of wine
Had helped thee to a Valentine;
A song in mockery and despite
Of shades, and dews, and silent night;
And steady bliss, and all the loves
Now sleeping in these peaceful groves.
I heard a Stock-dove sing or say
His homely tale, this very day;
His voice was buried among trees,
Yet to be come at by the breeze:
He did not cease, but cooed—and cooed;
And somewhat pensively he wooed:
He sang of love, with quiet blending,
Slow to begin, and never ending;
Of serious faith, and inward glee;
That was the Song—the Song for me!

Well, you're in trouble already if you 'do quite like him.' Consider this advice from the Bible at Proverbs 5:15-17 "Drink water from your own cistern And flowing water from your own well. 16 Should your springs be dispersed outside, Your streams of water in the public squares? 17 Let them be for you alone, And not for strangers with you."
That's a poem worth keeping. :)

He communicates through poetry. It was a nice gesture. I think you're craving social interactions, you're lonely. Yes, you can be lonely and married, especially if you and your spouse don't see each other often or no longer share things in common. Don't confuse companionship and romance. They each need different things to grow. He may just be literary. Don't lose a potential friend by making the wrong assumption.

He's conceited enough to tease you. Since the poem wasn't romantic, he might be toying with you to see what you'd do. Maybe he's just bored. Don't girls do that a lot? And your Q isn't about poetry but romance, so it's in the wrong category.

Here's how to tell how that married guy (at work) likes you:
1. He compliments you out of the blue.
2. He loves talking to you.
3. He tries to keep tabs on your love life.
4. He either shares details about his married life or refrains from doing so.
5. He goes out of his way to help you.

If he is liking/falling in love with you, then it is probably because of one of these reasons:
1. You might have the qualities that his wife lacks.
2. You might be making him feel whole again.
3. You might have re-installed his faith in love again.
4. You might have supported him during his critical times.

As you might be thinking how that married guy (at work) is actually more handsome than your own husband, then both of you might like each other. 
Popular love poems, from classic to contemporary, to share for weddings and anniversaries, on Valentine's Day, and year-round. These poems are perfect for to express romantic love, a lovely friendship, or a love that’s complicated.

Probably more than 'like'