Hellblazer Comics, First Issue: 1988 (though Constantine really first appeared in Swamp Thing in 1985) Supernatural Season 4: 2008
Kripke actually said he based Castiel's looks on Constantine which you can find out on the wikipedia page.1
There are rumors that he'd tried to get the rights to Constantine who could show up in an episode or two as part of the Supernatural 'verse, but since I can't find any good links for that, I'll just mention it and move on.
And, oddly enough, if they argued in a different direction, they would be accurate about visual theft...Constantine's appearance was, in fact, based on Sting.2 Of course, in the end, that would mean that their beloved Castiel's design is...second degree theft. Well, imitation is the sincerest flattery, they say...
Beyond this superficiality, though, there's very little in terms of character similarities. The worlds they live in are dangerous, dark places that'll soon backstab you if you give them a chance. Constantine's much closer mentally to Dean with his devil may care attitude, the drinking, the bedfellows, the quips, and most certainly the demons. And by demons, I'm not talking Nergal or Azazel, though those definitely play their part, but the internal demons (again, not the being possessed kind). The kind of demons that mean you have to drink to forget your dead brother (oh, yes, in Hellblazer there was one, if lost a lot earlier; check out Dangerous Habits or Hellblazer Issue 35) or startle awake with nightmares about Hell or Newcastle.
Oh, and there's the fact that both Sam and John have demon blood as part of what's running through their veins.
But there's another visual similarity I was struck with when checking out Original Sins last June (lgbt month; I figured it was appropriate). So I'll talk about that instead. Usual spoiler warning.
First, a pictorial comparison. (Both screencaps from things I own, actually.)
And the Doctor, specifically the Tenth Doctor:
The costuming caught my attention, and then I started thinking about the similarities. Both stand as a disruptive influence, challenging the norms and disregarding authorities. (Hellblazer usually goes further than just about anybody else, even in showing things on screen, including direct political commentary. Doctor Who is usually a bit quieter about its own forays into politics: Don't you think she looks tired?) If you wanted to go even farther, you could say both are examples of the Trickster archetype (Jung strikes again)3. Both figures are whirlwind bundles of ostensibly British chaos that sweep into a town and cause change. As expected with pure chaos and change, the good and the bad are about equally likely outcomes, and may in fact coexist. The Doctor often uses his title to ignore authority figures (although unlike Constantine if they've legitimately earned their title he's more likely to treat them with respect). In the end, they'll accomplish their goals (of saving the world), but not without sacrifice and maybe even a little of the absurd. Both push for critical thinking, not sheeplike behavior.
It's dangerous if you don't know about their worlds. It's even more dangerous if you know.
Both are haunted by the body count. "Just this once, everybody lives!" the Doctor calls triumphantly, and it's all too rare in Constantine's world, as well.
Both have an impressive 'I'm fine' facade, despite being haunted by their various internal demons. Only long acquaintances, usually, get the chance to see beneath, unless it's one of their more stressful adventures.
Both 'need companions' to keep them from their more self-destructive impulses. (But at the same time, it's dangerous to be around either one, no matter how brilliant it may seem.)
Both have impressive titles and unique 'powers'. Constantine is the world's greatest con-man. He's also The Constant One, the Laughing Magician, whose existence is to basically just be a thorn in the side of gods, demons, angels, and any other supernatural things with an interest in humanity. He has his magic, random magic relics, the occasional help of reluctant allies, and his knowledge. The Doctor is, well, the Doctor. His name is a title. The Oncoming Storm, the Last of the Time Lords, The Lonely God. He has the abilities of a Time Lord, Gallifreyan science, his sonic screwdriver, and his knowledge. The Doctor has the TARDIS, Constantine has Chas. More than that, though, the first weapon of the Doctor and the magician is their wits. Both have become famous for being able to outsmart their enemies.
Both also have pretty similar attitudes. They're both fairly cynical, though that could be because of all the messed up things they've seen. Nine especially is unsurprised (if disappointed) at the idiocy us 'apes' get up to, while Constantine, well. Watch an episode or read a comic and you'll learn pretty quickly that he expects humans to be selfish, backstabbing, capable of every sort of atrocity.
And yet, they're vast humanitarians. Humans, they don't believe in, but humanity? They'll put their chips on the table every time, and if it involves a fight to protect that spark of hope, of possibility they see? So be it. And because of the Trickster-type characterization they can pull off the impossible, if not without cost.
There are a few differences. The Doctor, as far as we've seen, doesn't smoke. Or curse like a sailor. Depending on the depiction he has almost Tony Stark-level panic attacks about the possibility of the Real Supernatural, as opposed to Clarke's Law tech. We don't see (or often, hear) about the Doctor's years of brooding about the emotional wounds of past battles. He can be worse than Constantine, though. (Don't believe me? Watch the pilot. That pilot. The very first one from 1963. No, not the censored version. The one where he was all for kidnapping Susan's teachers and in general was terrorizing them.)
In the end, Constantine is, perhaps, the Dark Doctor that writers keep trying to have and failing. (Barring Capaldi's Doctor, who I've not seen for my mental health since I've been eschewing Moffat writing after the disaster that was the Angels in Manhattan.)
3. Carl Jung. Not the best guy in the world but he had some really cool ideas that you owe it to yourself to check out. Archetypes are the biggest, including the Shadow and Persona, which, surprisingly enough, are drawn on heavily for the Persona series by Atlus.
(For those on the lookout for another Constantine look-alike, check out the Secret World cutscenes with Alex McCall. Aaaand he's still a better look-alike than the movie version. I enjoyed it but not as a Hellblazer movie. Not controversial enough, which works with the TV series because the character's the same even if the plot isn't, but to change both you might as well use a different name. Alex trailer: https://www.youtube.com/watch?v=