Yes, you can. In addition, you occasionally have service members who temporarily serve with another branch of the U.S. Armed Forces (like a liaison assignment) who may get an award from the other service. For example, I knew a Navy Medical Service Corps officer who was temporarily assigned to an Army unit, and who received an Army Commendation Medal that he wore on his Navy uniform.
BTW, I came into this thread late, but to address the OP…
Similar to what others have said, I can pretty easily read the ribbons for U.S. Navy (and Marine Corps) personnel, as well as the inter-service awards and decorations common to all branches of the U.S. military.
Someone whose decorations don’t make sense would stand out pretty readily (like a junior service member wearing a decoration or award typically only awarded to more senior personnel). Awards that are out of order would also stand out – note that awards are worn in the order of precedence listed here from top left to bottom right on a rack of ribbons.
BTW, note that for the awards of the Navy Command Master Chief Petty Officer shown in the link from the OP, there are four personal awards in the top two rows – the rest are unit awards, campaign/service medals, and marksmanship awards.
My father & grandfather were both in the Army, so I know many of the Army decorations. I don’t know very many USAF decorations at all.
My father, as a junior officer, served as the Aide De Camp to a General and ended up with some interesting ribbons for his then period in service.
First 25 years of service, he got 2.5 rows. Last 10, another 2.5 rows. As he says, when you reach General officer rank, they give it to you for breathing (except he did not say “breathing”).
Actually, it’s an olive branch crossed with a sword. The olive branch, naturally, bears a great deal of symbolism in Israel.
And it’s sword&branch with two fig leaves: Lieutenant General, sword&branch with one fig leaf: Major General (Aluf), and just the sword&branch: Brigadier General (Tat-Aluf). Israeli ranks are basically a streamlined mix of the U.S. and Commonwealth systems.
Also, different branches have different rules for which decorations can be worn. For the Air Force, you can wear most military ribbons, but any service-specific stuff for other branches goes to the back of the line after the Air Force ribbons. Any civilian ribbons or medals (such as Civil Air Patrol stuff) is typically not allowed at all, and a lot of the other types of decorations like marksmanship badges or shoulder tabs are typically not authorized either.
And even without knowing almost anything at all, there’s still some level of detail that can be read. For instance, the honor guard at my father’s burial (in a veterans’ cemetery) both had a large number of decorations, even though they were both very young (in their 20s or so). From their youth, I know they can’t have had very many of the “I was there” medals/ribbons, so they must have been individually awarded. Individually awarded what, I couldn’t say, but a lot of whatever it was.
Although, by about four years in, an airman might have been in long enough to pick up service medals for three places (let’s say he started at a nuke base for a Nuclear Deterrence service medal, then went to Korea to get the Overseas Short and Korean Defense Service Medal, then maybe got sent to another base with an associated service medal.
If he’s pretty solid, he probably got Achievement Medals for end-of-tour at his first two bases, plus maybe he deployed to pick up something like the Afghanistan Campaign Medal and another Achievement medal (note that additional Achievement Medals on USAF uniforms are denoted by devices on the first award, not multiple ribbons). On the way he got National Defense Service, Air Force Training, GWOT Service, Longevity, and Good Behavior (yes really) as a given.
So after four years, he’s got 10 distinct ribbons (plus devices), making for three rows plus an extra ribbon, for presumably being solidly good at whatever he does plus getting a short tour overseas.
This presents a good segue for the differing tendencies of the various branches of the U.S. Armed Forces to give out personal awards. The conventional wisdom is that the four branches give out personal awards as follows, from the most reticent to the least:
[ul]
[li]USMC (most stingy with awards)[/li][li]USN[/li][li]US Army[/li][li]USAF (hands out awards like candy) :rolleyes:[/li][/ul]
The USAF, for example, actually gives out an award for completing initial accession training. :rolleyes: The Air Force Training Ribbon is held is such low regard by the other services that is actually prohibited on all USN and USCG uniforms worn by former USAF personnel. (Which evidently contradicts my response back in Post #81 – apparently, it is up to each branch of service as to what awards can be worn from other services.)
In Raguleader’s example above, his hypothetical junior airman has received two end-of-tour Air Force Achievement Medals. This would be extremely unusual for a junior enlisted in the USN. The nominally equivalent award, the Navy and Marine Corps Achievement Medal (NAM), would only be awarded to junior enlisted personnel in extraordinary circumstances. (A NAM is instead more commonly awarded to junior officers and senior enlisted personnel.) The wikipedia entry here discusses the reason why:
Similarly, the Navy and Marine Corps Commendation Medal is considered more prestigious and less frequently awarded than the nominally equivalent Army Commendation Medal, which is also noted in the wikipedia entry for the award.
Roughly speaking, where USAF and US Army personnel get Achievement Awards, Navy and USMC personnel get letters of citation (no award). Where USAF and US Army personnel get Commendation Awards, Navy and USMC personnel get Achievement Awards. This tends to continue up the precedence list, so you tend to end up with USAF and Army personnel with far more awards than USN and USMC personnel.
Human nature being what it is, these differing practices between services leads to Marines scoffing at USAF airmen with their rows and rows of ribbons. 
I don’t know the uniforms well enough to say, but I don’t think that the honor guards I saw were airmen. Would airmen have been acting as the honor guard at a sailor’s funeral?
If that’s who was available to go, could be (an Army vet at our church had a Marine detachment for his funeral last year). I think the Pentagon/DVA tries to send personnel of the same branch as the deceased, though.
When we buried my Dad [Army was a full colonel when he retired], we had mrAru [full dress whites, it was summer] 2 Marines, 2 Army and one lonely Air Force kid and about 2 dozen dangerous old codgers [some WW2 combat infantry, some Korea era combat infantry and 3 Vietnam era Rangers. Wouldn’t have been a good bunch to surprise by trying to mug them]
I know mrAru used to do the whole notification thing, and did the graveside thing a fair amount, Sub Base New London had a territory that was fairly large. I think they actually had like 3 teams for the graveside thing.
Could have been worse, on the Spadefish they ran out [wonder if it was the same chop?] and popped up near some scientific bunch and hijacked their resupply flight. mrAru said they were even out of peanut butter by that time.
Were you there for the Beef ‘Rolaids’ debacle? How bad is a rendition of a standard recipe to get it banned from the boat menu:dubious:
ROTFLMAO - you assume that officers are competent. How sweet.:rolleyes:
There is a sort of process for it all. The senior enlisted in charge more or less works of a standard supply list [he gets to add some special stuff like if the CO like lingonberry jam they might throw a few jars onto the list] then the Chop goes over the paperwork and signs off on it, then passes it up the chain of command and it all gets ordered and the ‘cost’ deducted from the deployment financials. The process sort of fell apart [one cruise mrAru overheard the chop saying that he refused to have men walking on cans … it wasn’t suitable for a fighting ship. sigh] So they only had food for 3 months instead of 4. Sucky.
mrAru said he was thrilled at that point he had stashed a bunch of geedunk in his rack - as memory serves his normal load out was 6 of the large bags of hard individual wrapped candies, 6 pounds of beef jerkey and 2 boxes of the peanut butter cheesy cracker snacks. I still think he must have slept wrapped in something hanging by his toes vampire fashion in a corner somewhere, I remember going below on the Miami and his rack was full of snacks and spare parts.
Thank you.
Makes life interesting for the guys in the bottom racks, too.
I remember helping transfer stores forward from the engine room on of my deployments, though I can’t remember which boat it was.
:D:D:D;)
aruvqan, as I recall, LSLGuy was an officer himself.
robby, how did you end up crossing the date line? Crossed under the Ice cap maybe?
While the Air Force may give out awards like candy, I will point out that in return, we get the worst uniforms of the whole bunch. 
At least USAF has done away with the silly airline-pilot lookalike version. Fortunately I was out before that buffoonery had its day in the sun.
Strictly speaking that was RAF style insignia. Since the USAF did follow the RAF blue when it separated from the US Army, insignia were only fair.
Now grow a proper moustache, Flight Lieutenant!