Thirteen reasons to watch Bleach? I think I can rise above the usual "hollow ichigo soooooooooo awsum!!!!!!!!1!!!!!" for this one.
1. It's Bleach
Seriously, it's one of the "Big Three". You really ought to watch it, if for no other reason than it's damn fun to watch and it's so much a part of contemporary anime. What more can I say?
2. Music
Know who does the music for Bleach? A man named Shiro Sagisu. Does that name sound familiar? If it does, GET HELP, because you've been spending too much time on the Internet. Shiro Sagisu was also the composer for that omnipresent legend, Neon Genesis Evangelion, so the guy's not exactly an amateur. Each arc goes through distinctive musical styles, from the experimental/techno/there-are-words-to-describe-this-but-I-don't-know-what-they-are during the beginning to reflect Bleach's musical roots, to the Spanish and Mexican-influenced tunes of the Arrancar arcs, to the all-out orchestral onslaught of the movies. No matter what you like, Bleach has a song for you.
Love it.
3. The Soul Society Arc
So shounen shows like Bleach, Naruto, One Piece and the like get a bad rap, and for legitimate reasons. But man oh man, if you can't enjoy the Soul Society arc there must be something wrong with you. It's simply so powerful on so many levels. It's all hinged on an execution no one seems to approve but all seem powerless to stop. Why is Rukia's brother not only willing but determined to ensure her execution is carried out?
Who murdered Captain Aizen and why? The Soul Society arc spins not only the emotional tale of Ichigo trying to save Rukia, but at the same time it tells a plot-driven narrative while simultaneously fleshing out the Soul Reapers, Ichigo's enemies. And in the end, it brings them all together...
4. Symbolism
Would you believe me if I told you the Soul Society arc is about cultural revolution? Yeah, that's right, you thought you were watching a show about guys with magic swords and it was actually getting all literary on you. How 'bout dat? What's that? You don't believe me? Well let me explain...
The Soul Society arc is all about old Japan vs. new Japan. The Soul Society is a sterile, stagnant society run by powerful aristocrats who can't even be bothered to care about the human world. Byakuya embodies everything that Soul Society is. An inflexible, cruel aristocrat more concerned with the pride of his family and the Soul Society than the life of his family. And what's his sword?

Senbonzakura..."One thousand cherry blossoms". Perhaps nothing is more iconic of traditional Japan than cherry petals drifting on the wind.
That is Byakuya Kuchiki.
And our protagonist?

Ichigo is Byakuya's opposite. He's young, inexperienced, loud, rude, and operates only by his own morals, not anyone else's. His hair (although apparently natural) is the color associated with delinquents and gangsters. Even his weapon, Zangetsu, is more of a meat cleaver than a sword. Compare that to the perfect of grace of Byakuya, who can kill without his opponent even knowing he's drawn his sword. And what about Tensa Zangetsu, Ichigo's Bankai and the ultimate expression of his heart?

An slender sword. An ordinary sword for an ordinary person. This is no "Vibrant Display of 1,000 Cherry Blossoms". It's a mockery of Byakuya's pride, the pride of Soul Society.
"Our pride’, you said? So that pride you're saying to be so precious, is that connected to killing Rukia? Is it? Then I should stomp on it as you said. 'Cause that's why I obtained this Bankai!"
5. This scene

You weren't expecting me to be
all serious, were you? But how awesome is that? He stops Ichigo's sword...with his finger! And then...booooooom!!!
6. Ulquiorra Cifer

Many people, including myself, feel the Soul Society arc was Bleach's highest point, but there's quite a bit of amazing material afterwards as well, a lot of it centered around Marilyn Manson...er, I mean Ulquiorra. The gap in strength between him and Ichigo is insurmountable. His outlook, logical yet mysterious. Truly a worthy rival. Oh, and of course...
"I see. This. Yes. This thing in my hand is the heart?"
7. Tite Kubo knows how to raise the goddamn stakes
Anyone else remember
this moment?

Oh I'm sorry, did you think Ulquiorra was the strongest Espada? NOEP. He's not even second, but
fourth.
8. Aizen taking off his glasses

"It looks like my murderer...*glasses*...just got caught."
9. Tite Kubo is a hack writer and should be **** **** **** in a **** **** with **** **** **** **** and stain remover
What, does that not sound like a reason to watch Bleach? Just because Tite Kubo, the manga's author, doesn't think more than half a chapter ahead, thus turning the plot into a ridiculous mess, doesn't mean you shouldn't watch it. It's like watching a giant explosion in slow-motion. And then gradually realizing it's your house that's exploding and for a moment you're horrified, but then you realize your family's right next to you and everything's fine. I'm not sure if the house represents Bleach or Kubo himself.
10. Coyote Starrk
all you kids wanted a guy with a gun bankai here he is now shut up

Starring the Sundance Kid as "Coyote Starrk"!
11. Uh...Zaraki Kenpachi?

People seem to like this guy. He's pretty cool. He's a psychotic murderer and doesn't afraid of anything. And he doesn't die when killed, contrary to the claims of certain Internet memes. He's also the cause of this rather dramatic scene...
12. 366 episodes
366 episodes x 20 minutes = 7320 minutes = 122 hours = about 5 full days
You know those times in your life where you're like "I have 40 minutes, but nothing to do". Say goodbye to those times.
13. The show has a strong, nuanced female character

The Internet's all up about sexism recently (and by "recently" I mean for the past year at least, and into the foreseeable future), so I thought I'd throw this one in to wrap things up. Okay, so for the first arc she's lost her powers and for the second arc she's...kidnapped...but
after that she can fight alongside everyone else. And her sword is pretty awesome. On top of that, she has an extraordinary and very moving battle during the Arrancar arc.

Jesus
Christ. No punches pulled there.
And that's 13 reasons why Bleach, for all its flows, is damn awesome and you should watch it. Peace.