I have a Valentine 1. It cost me $400 about 9 years ago, and it probably saved me from about one ticket every year, which I would definitely consider worth the price. On the other hand, I have gotten three or four actual tickets in that period, so it is not foolproof. Most of those were from cops using laser on the highway.
While laser and instant-on radar are used a lot on the highway, a lot of cops have vehicle-mounted radar guns, which they will leave on while driving, or just while parked on the side of the road. The V1 works great for those - it is very sensitive (sometimes alerting you several miles in advance), and the directional arrows are a must-have for ruling out false alarms.
False alarms are definitely a problem, but once you’ve used the thing for a while, you learn to distinguish the pattern of a false alarm from a genuine signal. I mounted mine at the top of my windshield, right next to my rearview mirror, so that I could easily see the lights, and generally kept the volume turned off.
It is technically possible for your detector to detect even instant-on radar and laser guns, if the cop aims for the car in front of you first and you pick up some of the scattered signal. Obviously, if you’re the only car on the highway, you can’t depend on that.
The other major radar detector brands are worthless, in my opinion, because they don’t have the arrows. Cordless detectors are especially worthless - to save power, they do not run the receiver circuit all the time, and so they are less sensitive and take longer to alert than corded models.
Radar jammers are illegal in all states, as radar emissions are regulated by the FCC. Laser jammers are widely available, however, because they use simple infrared LEDs, which are not regulated. I considered buying one, but decided it was best not to enable my speeding habit any further.