I do not think about alarms and early warning systems too often: they just exist and are largely ignored, until... Every now and again one really makes a difference in my cruising life: so I cobbled together this list: I am sure I missed a few.
My best, Dick Stevenson, s/v Alchemy
I would suggest that there should be a handful of early warning systems that a skipper should install. This goes especially for recreational skippers and even more so for those who sail as a passage-making couple. The benefits of an early warning do not always jump out at you. Many of the following early warning systems are warnings where vessel integrity and crew safety are at risk. Early warning puts skipper and crew in a pro-active position rather than reacting to, say, the floorboards being awash where it is likely already too late to enact a remedy. Some early warnings are crucial (propane leak) while others are a flag to attend to something later (slow leak of coolant). But every early warning allows for remedies and intervention when the intervention can still make a difference.
A few minutes of early warning can be the difference between saving the ship or abandoning her. It allows a period of thinking rather than a quick journey into panic. Many emergencies on board escalate quickly: easily dealt with at the onset they can quickly become unworkable: early intervention makes a huge difference. All audible alarms should be able to give warning to crew in the cockpit when the motor is operating. In the scheme of things, these units are not expensive nor do they demand much in the way of battery usage to run 24/7 (some run on their own battery).
Early warning systems on Alchemy:
1.    *Smoke detectors (combined unit with CO detectors): engine room, above electrical panel and in the forepeak (sleeping) cabin.
2.    *High water alarms: Alchemy has two, one in each of her isolated bilge areas.
3.    *Propane sniffers: Alchemy has two, one in each of her isolated bilge areas.
4.    *Bilge pump alarm: every activation of the bilge pump
5.    *Diesel and generator alarms: oil pressure and temperature (alarms rather than idiot lights)
6.    *Raw water failure alarm (Borel) on engine and genset
7.    *Dedicated CO detector (CG required, I believe)
8.    I have a very quiet ship, but I have never completely tamed the lines that raise and lower my pole on the mast: at 20-25 knots of wind from the bow at anchor, they slap the mast. This is my wake-up call to check things out.
9.    One’s senses: especially ears. Pay attention to new noise/smell etc. and changes in regular noise.
Early warning systems requiring inspection:
1.    There is a small dam downstream from the engine and genset where any leaked fluids accumulate: a quick opening of the over-the-engine access hatch allows a look.
2.    My dual Racor filter assembly has a vacuum gauge which can give early warning of filters becoming loaded and blocking/slowing fuel delivery and other forms of fuel constriction. (some have an alarm indicating water in the fuel).**
Do not have (or use) but may be wise:
1.    A low and high voltage alarm (or SOC/state of charge alarm)
2.    Various instrument alarms: AIS, Radar, depth, etc.
3.    Anchor alarm
*In my opinion, these should be required to be installed by the manufacturer when installation is far easier. I would suggest every boat should consider installing these alarms.
**Highly recommended on a widely ranging cruising boat
Caveats:
Alarms are a good thing. They warn of emerging problems and they do not get tired or lazy.
That said, I think many would agree that we have so many alarms, that when one goes off, it is hard to know what the warning is or where to go to respond. Someday, an enterprising entrepreneur will come up with an alarm annunciator: in the meantime, it behooves every skipper to make a “vessel alarm list” and to try to differentiate the alarms by sound (buzzer, beep, two-tone, etc.).
Then, highlight the “urgent” alarms: on Alchemy these are: engine oil pressure & water temperature, high water, bilge pump activation, propane sniffer, smoke detectors, exhaust hose temperature, and CO. Then there are the skipper-set alarms on AIS, radar, instruments and the DSC alarm on your VHF. And finally, there are the alarms that emerge from our “devices”. Post this list where it is easily accessible to remind/review (wall of the head?).
One danger with alarms is that they can support a false complacency that inhibits regular inspections. For example, an eyes-in-the-bilge inspection should remain an every-watch occurrence during passages. Also, a reminder: many alarms need attention. Some beep when batteries are low: some do not. A beginning-of-season renewal of all alarm batteries is wise. Other alarms have expiry dates (CO are often 5 years) while smoke detectors can malfunction because of accumulations of dust or cobwebs. One’s confidence in propane sniffers increases when it activates when tested with gas from an (unlit) lighter.