Probably the most widely used modulation effect is chorus. Chorus is designed to "fatten up" sounds by crudely simulating the way an ensemble of instruments might sound. When you have a group of musicians playing or singing the same part at the same time, even if they're using identical instruments, there will be some slight variations from musician to musician in their timing and tuning. This is concept is why a string orchestra sounds "bigger" than a quartet instead of merely being louder. Chorus effects mix the original signal with small amounts of delay and variation of the pitch, usually created with an LFO. The result sounds different than if you had multiples of the same instrument playing at once, but it's still quite a pleasing effect, adding width and warmth to the effected sound. Chorus is commonly used on guitar and vocals, and was an extremely common effect to be included on many of the DCO polysynths in the 80's that lacked the huge unison effects so common on synths today. Here is an example of what it sounds like:
Flanging is an effect that was extremely popular among guitarists in the 70's. Before the dedicated effects units existed, audio engineers would create the effect by running two tape machines playing the same audio materials and altering the speed of one of the machines by gently placing their fingers on the flange of the tape reel. The effect became so popular that dedicated flanger effects that simulated this technique were created. These worked by mixing the original audio with a copy that is being delayed by a varying amount. The sound of flanging could be described as "wooshing" or "sweeping". It works great on guitar (especially if you are after a retro sound), on entire sections of a mix as a special effect, or on anything that has a lot of high frequency content or noise to add instant movement. The "train" sound at the beginning of Kraftwerk's "Trans Europe Express" is a good example of this. Late night paranormal radio show host Art Bell was famously such a fan of the effect, that Billy Gibbons from ZZ Top had a CD player with a built-in flanger on the outputs especially for him! Here's what flanging sounds like:
Phasing is sort of like flanging's more mellow cousin. It produces similar sweeping effects, but is noticeably less nasal and aggressive. Phasing works by mixing the original signal with a copy of that signal that is having its phase modulated. This effect was a favorite among keyboardists in the 70's and 80's, especially on electric piano and string machines. The strings in Jean-Michel Jarre's "Oxygen Pt. 1" are a great example of the effect in action. Here's what it sounds like on our guitar:
Although these are the most common modulation effects, they are by no means the only kind. The thing to keep in mind with these effects, as with any effect, is that there is no one "sound" you are restricted to. By varying the parameters in your DAW's modulation effects, you'll find an amazing amount of variation within these seemingly simple effects.