Is there ever a reason to not declare an emergency if you believe something is happening in/on/around your aircraft that could likely result in injury to the pilot/passengers or damage to the plane?
I understand the concept of crying wolf. But if something had you seriously concerned and you declared an emergency, only to find once on the ground that it was nothing, would there be any repercussions? Assuming that the landing was normal in all respects, other than the declaration of an emergency.
You won't get in trouble for making a declaration of emergency anywhere in the world, however, one ought to have a belief in a bonafide emergency, or have an actual emergency prior to doing so.
The concept of "declaring" is misunderstood and often misapplied. The point of making such a declaration is to request priority with ATC. There are times when one makes such a call in the blind, such as a mayday or pan pan call, but generally there is no benefit to declaring for the sake of declaration.
"I declare thee therefore this day, thou art an emergency!" does little good.
If you have a problem, contact the party which can most help you and state your problem. Get to the point, and don't be too worried about making a formal declaration.
Several years ago in a high performance twin turboprop, I had a complete loss of oil pressure during a departure. I notified ATC of the issue and stated my intentions; returning to land. No formal "declaration" was necessary, and I did not make one. I shut the engine down during the descent, and continued to a normal one-engine landing. Upon arrival, I was met with crash rescue. I did not request them, but the tower did, and that was fine. It was a very simple process.
A couple of days ago I got a fuel filter light just after takeoff, and jettisoned my load. I notified the aircraft ahead of me that I was jettisoning with a filter light and returning to land, and then I turned around and landed. The aircraft ahead of me notified the air attack over the fire of my situation; I did that primarily because we were working a structure that was about to be burned over, and I didn't want them expecting another tanker that wasn't coming. No declaration of an emergency was necessary, nor made. Making such a declaration while departing the uncontrolled field wouldn't have benefitted anything at all. At most, I could have made a request with the unicom to call the airport fire rescue personnel, but it wasn't necessary and I didn't.
Conversely, while landing a turboprop single tailwheel airplane in a strong crosswind a few years ago, I discovered that I had no hydraulics. Without brakes, the airplane would have departed the runway, and the prognosis wasn't good at that location. I picked another airport, notified the dispatch center of my condition and asked them to notify the aircraft operator. I went to the other airport, but the runway I needed was closed with men and equipment on the runway. I discussed my condition with the tower, determined that the men and equipment could be moved and that the runway was able to bear my weight, and notified ATC I'd use the closed runway anyway. They had the runway cleared, and the problem was solved. No emergency was declared. I told ATC what my intentions were, and ATC offered what assistance they were able.
Where one ought to declare an emergency, one ought not delay, and one should never do so for fear of repercussions. It's not illegal to have an emergency, just to create one. Take care that you don't create one by making a big deal out of a small one.
A crew years ago was having a hard time getting a word in edgewise, and finally broke into the ATC mix with "XXX Approach, XXX is down to one engine and three hundred pounds of fuel. Request immediate landing!" The crew was granted an immediate, and all other traffic resequenced to get them in. The tower then watched a single engine Cessna with full fuel slowly make it's way down final to a normal landing, with a crew of CAP volunteers on board. They got an earful. By making such a foolish statement, they put a number of other aircraft in jeopardy and created fuel situations and diverts for aircraft carrying a lot more people, burning a lot more fuel, and that had priority over the Cessna. It's okay to declare an emergency, but be sure you have one to declare.
If you're in doubt, make the declaration and sort it out on the ground.
UPS 6 didn't make such a declaration soon enough after departing Dubai last year. They were on fire and bypassed Doha, when they should have been getting on the ground. They were unable to see anything on the descent, missed the approach and ended up crashing outside Dubai. If you have a need for priority, seek it early and get on the ground where you can handle it safely. Then worry about whether you should have done things differently. It's not nearly so easy if you wait too long.
Engine failures are easy too...always an emergency. Loss of cabin pressure and you can't keep the cabin below 10,000? Emergency. Above 10,000 non-pressurized and you lose O2? Emergency.
An engine failure is not always an emergency. In many cases, it's a non-event. In many others, it's not even in the emergency procedures; it's an abnormal event. You perhaps ought to qualify such statements a little more.
Loss of cabin pressure...it can be an emergency, but not necessarily so.