Training tools that everyone should use, in my opinion, are tools that provide metrics on how you are doing. I have used both the SportCount lap timer and the Tempo Trainer. The SportCount provides me with feedback on how I've done (e.g., in multiple length sets, how did my swimming speed change from length to length), while the Tempo Trainer provides ongoing feedback while I'm swimming.
The important thing to be aware of with other training tools is that all of them change the swimming equation in some way, so you want to know how each one is going to change the equation and whether the change is going to benefit you when you're not using the tool. And you shouldn't use any tool all the time (one of my criticisms of drag suits, for example, is that people who use them typically put them on and wear them for an entire practice, and sometimes for every practice).
One tool I don't recommend is a kickboard. When I came to TI in 1999, I had a wide, flailing kick, and I had developed it from doing kicking lengths with a kickboard. The problems with this are:
1) When you're leaning on a kickboard, propelling yourself using nothing but a kick, your body is held in an unstreamlined position which creates a lot of drag, and with nothing but a kickboard to propel you, you're desperate to move. The flailing kick I had developed was powerful, but not streamlined, but the fact that it was unstreamlined made little difference, considering the fact that my whole body was being held in an unstreamlined position by leaning on the kickboard. The trouble was that the kick I developed from this was actually slowing me down when I swam freestyle because the kick was so unstreamlined.
2) Leaning on a kickboard is a crutch to enable swimmers to breathe while they're doing kicking sets. It is possible to hold the board in front of you and keep your face in the water, but if you're going to do that, why use a kickboard at all? It's much better to kick in a skate position, where you will be practicing balance and streamlining, and will also naturally develop a streamlined, rather than a flailing, kick. And if you want to practice just kicking, vertical kicking is a much more effective drill.
Fins can be a useful tool for some beginners to use some of the time. When I was getting over my flailing kick, for example, the only way I could overcome it was to focus on literally nothing else. But if I put on fins, my kick would immediately settle down, allowing me to focus on other aspects of my stroke. Fins can also make you move faster in the water, which can make you more sensitive to any lack of streamlining in your form. But if you're using them for that purpose, you should only use them for a small portion of your practice and take them off the rest of the time.
I don't recommend hand paddles, because they artificially enlarge your hands and tend to make you rely too much on your hands for your catch, which is likely to make it hard for you to hold onto the water when you take them off (as you inevitably must when you're in a race). And they make it easier to put too much stress on your shoulders and injure yourself.
A better tool for improving your catch is fistgloves, which essentially do the opposite of what hand paddles do. Being deprived of the use of your hands forces you to learn to grip the water with your forearms, encouraging you to develop an early vertical forearm (EVF) or as close an approximation to it as your physiology allows. The gloves also create a kind of sensory deprivation, so that when you first take them off, you become very aware of how your hands are entering the water, how they're grabbing onto the water, etc. And when you take the gloves off, you are likely to find that you're now gripping the water with both your hand and your forearm, which will make your catch more effective. Be aware, though, that you may swim a little slower when you're drilling with fistgloves, which can make you less aware of ways in which your body is unstreamlined. So don't wear fistgloves all the time. A good procedure is to wear them for the first 20 minutes of your practice and then take them off for the rest.
I've never used a snorkel or felt any need to use one. But some people who are having trouble mastering breathing find that using a snorkel allows them to work on other aspects of their stroke without needing to periodically stop and catch their breath. As long as they're spending part of their practice without the snorkel, working on mastering breathing, I don't see any problem.