Finally -- a topic I know about!
First, what machines? It matters because small ~1hp and less machines can get manual starters, esp. if the motor has builtin protection and/or you aren't going to work it to death. Many machines in the '50's and '60's used Arrow Hart lightswitch style, which can handle 1.5hp or 2hp single phase 110v depending on the model. They look like this (Often seen with a cooler red badge):
I like this style on small machines. If you look around, you can find them for $20 with some frequency. They are still made I think, but by Crouse Hinds (and possibly in Mexico rather than USA).
Here are some more styles, including a Furnas model 44r reversing drum switch:
Pay attention to the NEMA size. I usually look for NEMA 1, which will do up to 1.5hp on 110v.
Furnas, Square D, Allen Bradley, Cutler Hammer, and others made similar manual motor starters, some with cool buttons instead of a lightswitch-like switch. You don't get any motor overload/burnout protection. Some newer motors have a rudimentary type of overload protection built in, so these motors are a better match for these manual starters.
Anything more than ~1hp should really have a mag starter, possibly with a remote switch to control it. Some people think every machine should have one, regardless of size, but they can be a bit large/cumbersome.
The general idea is that when you push "on" you energize an electromagnet, which magnetically pulls the contacts together you get power to the machine. If you push "off" or the power goes off, the magnet stops being energized and the circuit breaks. In other words, "on/off" is just a momentary low current switch that powers this electromagnet, and the electromagnet is the "real" switch that handles the large load of the motor. So, this gives you a ton of options for the actual on/off switch, as these are just momentary switches. This system is good because your machine won't restart unexpectedly when the power goes back on after an outage, and also, it can reliably turn off much larger motors. Also, mag starters let you install "heaters" inside, which monitor the current draw of the motor (a bit like a fuse or circuit breaker) and shut it down when you are overworking it so you don't fry your nice big motor.
Allen Bradley 609 is one of the industry standard mag starters, and you'll see various versions going back 70 years (earlier ones have rounder boxes). They have 3 letters after. The "A_ _" models are smaller (NEMA 0) and the "B_ _" models are larger (NEMA 1).
Allen Bradley 709 is similar, but usually used with a remote on/off low voltage control. Lots of cool/vintage looking ones are available, or use any pair of "normally open" and "normally closed" switches designed for low voltage control.
Here are a couple of control switches used to control a mag starter:
Also, This is how the big mushroom switches on some industrial machines are wired, i.e. mushroom just controls the mag starter. Personally, I think this system is one of the safest possible, and is a sort of industrial version of the manual paddle switch someone posted above.
Search "Rees Mushroom Switch" on ebay for one classic version.
*Note: pictures linked are from ebay & owwm.org. OWWM has a few threads dedicated to coolest vintage switches -- may be worth a search!