The question is fairly straightforward, although I’m sure the answer isn’t. If one has blood in their stool, urine, or phlegm, which is typically a more serious cause for concern? Am I leaving out any obvious bodily fluids… (semen perhaps?)
IANAdoctor, and the severity of the bleeding is more important than the site, but I’d say digested blood in your stool (melaena; black, tarry stool) is potentially the most urgent. Bleeding from any of the three sites has potential causes ranging from the completely harmless to malignant cancer. Of course, coughing up blood could be a symptom of pneumonic plague, which would be bad news indeed 
Need answer fast? Are you bleeding from all three? Have you been eating rat poison?
Oh, and you left out haematemesis, vomiting blood.
Well, all of them are most likely to have a benign, or pretty harmless, cause.
[opinion, without cites, follows (and is based on the assumption that the person isn’t on blood thinners)]
The most common cause of blood in the stool is hemorrhoids. And, supposedly, good old bronchitis is the likeliest aetiology for blood in the phlegm. In women, a urinary tract infection underlies more cases of blood in the urine than anything else (except, maybe, menstrual blood), whereas blood in the urine of man is most likely from benign prostate disease.
If I had to guess, which, among the three forms of bleeding mentioned, is most likely to have a serious cause, I’d venture that blood in the phlegm is #1. The the top three nasty things in that case probably being pneumonia, cancer, and TB (or maybe a pulmonary embolism, i.e. blood clot to the lung).
There are many causes, of course, for all three symptoms. Blood in the stool can definitely indicate a bowel cancer but things like benign polyps, diverticular disease, and colitis (either infectious such as salmonella, or inflammatory like Ulcerative Colitis), are more common. Likewise, blood in the urine can be due to kidney cancer, but stones and, as mentioned, infection, are more likely.
It is also critical to note that the answer to the question is hugely affected by the age of the person, any associated medical/surgical diseases, their habits, medications, and whether the blood is grossly obvious or is apparent only on lab testing.
ETA:Hematemesis, as toodlepip added, is ALWAYS serious even if from a benign cause like an ulcer.
No, I don’t need the answer fast. I haven’t eaten rat poison since the noodle incident. Thanks for your concern 
I believe that sweating blood is worse. I don’t want to know if I’m right, though.
For those interested, I was taught that blood in the ‘ejaculate’ is usually from an inflamed prostate or inflamed seminal vesicles, and also, apparently, can be just spontaneous, with no identifiable cause (i.e. “idiopathic”).
What KarlGauss said, not that he needs my 2c to confirm his excellent post.
For urine there’s gross blood and microscopic blood (gross blood means obvious blood). Urinary tract infections and kidney stones are common causes of microscopic blood in the urine. Gross blood (obviously bloody urine) particularly if painless, would make me think bladder or renal cancer, so not a good thing.
For stool there’s gross blood, microscopic blood and black blood (blood that’s been exposed to hydrochloric acid).
Gross blood is most commonly hemorrhoids, anal fissures or a little busted blood vessel in the colon. Usually benign. Microscopic blood can be anything; in the presence of anemia it’s suspicious for a colon cancer which oozes a little bit of blood chronically. Not good. Black blood (melena) usually means the source of bleeding is in or near the stomach (stomach acid turns blood black), and usually an ulcer (assuming the guy doesn’t have cirrhosis or something). Not a big deal. And you can poop fairly reddish stool if you are bleeding a lot from an ulcer. Not a big deal if you get the bleeding under control.
For phlegm there’s bloody phlegm associated with what sounds like a respiratory infection. Not a big deal. Then there’s the guy who starts coughing up blood for no good reason. That’s often lung cancer or a blood clot to the lungs. Not good. Not good at all.
There’s vomiting blood. Usually an ulcer. No big deal.
Now all of these are just average things we think about, as KarlGauss points out. There are hundreds of causes of various types of blood from pretty much everywhere, and the causes range from the trivial to the “Pardon me while I exsanguinate while you are examining me.”
Overall, my experience tells me gross blood in the stool is the commonest, and usually benign (infection; hemorrhoid; angiodysplasia; fissure…).
Gross hematuria and grossly bloody phlegm are not common; I’d guess grossly bloody plegm in the absence of what sounds like a pulmonary infection is probably the most immediately serious, but the guy who comes in peeing pure blood likely has a malignancy (although we do sometimes see relatively painless kidney stones or benign causes).
Yep, for two of my six kidney stones, my urine turned black from the blood, and I wasn’t in any pain at all at the time.
The noodle incident??
Bodies are gross.
I apologize for the content-free post, but man. They’re just really, really gross.
–Cliffy
Well there’s Haemolacria
Cough - that closes down Madagascar faster than anything. 
Heh. It can also come as a bit of a surprise to your girlfriend who is post-menopausal and you’ve just undergone a prostate biopsy.
I’m sorta used to medical ickiness, but that’s just gross.
Good point (both of them!).
Absolutely. But, then again, I hear it often comes as the climax in vampire porn.
I have a friend who made the enormous mistake of, upon finding blood in his urine, Googled it while waiting for the doctor to fit him in. Do NOT do that if you’re of a nervous disposition.
It turned out to be a prostate infection, actually. They figured that out after a week of peeing through a sieve assuming it was kidney stones.