The line between Blues, Rock and Metal can be "fuzz"ier than you'd think.
Effects can be broken up into three classes: Gain, Modulation and Time (GMT), and roughly, they are placed in the chain in this order.
(If you place things out of this order and like the sound, you are under no requirement to change.)
In the Gain section, Distortion occurs when the smooth wave of the signal gets "clipped" because the circuit cannot handle the signal. You can do this by using higher-output pickups, putting a pedal before the amp that forces it, boost the signal with a pedal going into the preamp, boosting the preamp to get the power amp distorting, and pushing the speakers to where they break.
Also involved is compression, where the volume difference between playing hard and playing soft. One big benefit from compression that you don't get from fuzz is sustain. The longer the note goes, the more voice-like or violin-like a note can be, and part of why guitar has been so popular in the last 50 years is that electricity has allowed it to sustain and sing.
(Far more about these points can be found elsewhere here, and also all around the Internet. Distortion and compression are much of what guitarists want to talk about.)
With pedals, the distortion and fuzz pedals give that square wave without necessarily adding signal, and overdrive and boost pedals amplify the signal without necessarily altering the wave.
There are great guitarists who use pedals to get their distortion. There are great guitarists who essentially plug right into the amp.
Modulation is changing the characteristics of the sound. Tremolo, vibrato, chorus, phase and flange are prime examples, as is the wah, although generally, the wah is placed as the first pedal after the guitar. I think you'd categorize pitch shifters and octave splitters here, too, but I'm not sure if you'd generally put octave splitters before or after fuzz...
Time effects are generally reverb and echo/delay. If you have a volume pedal or kill switch, you generally put it before the time effects, so that swells and repeats are not stopped when you silence the signal.
There are certain artists who are known for certain classes of effect. I associate Jimi Hendrix with the wah, U2's the Edge with delays, Dick Dale with excessive amounts of reverb, Tom Morello and Jack White with the Whammy Pedal pitch shifter, and Andy Summers of the Police and lots of fusion players with chorus. I don't associate metal with time effects much, as this would tend to muddy up the fast rhythms.
Specifically with worship, there was a point where the CCM/Worship guitar sound was Journey, followed by U2. Lately I'm hearing and playing lots of pop-punk influence -- basically crunchy guitar without much modulation or reverb/delay -- plus some folky bleedover from Mumford and Sons, but your congregation may vary.
But, given any effect, there is likely a player in any genre that uses it to great effect.