I have recently been lucky enough to complete three "rainbows"...
2009 Bowman Sterling WBC Relics Miguel Tejada

Regular, Refractor/199, Blue Refractor/125, Gold Refractor/50, Black Refractor/25, and Red Refractor 1/1
I don't usually pick up non-A's Tejada stuff, but when I saw the Blue Refractor version of this card at a show last year I had to have it, because it just looked awesome (the scan doesn't do the Blue, Gold, and Red cards justice, they're beautiful). I picked up the other versions on eBay and COMC, and last week the Red popped up for auction. I put in a high bid (for me) because I really wanted to complete the rainbow, and won it for half of what I was willing to pay: $22 delivered.
2012 Bowman Ted Lilly

Base, Gold, International, Blue/500, Orange/250, Silver Ice, Red Ice/25, Red 1/1
This was almost the reverse of the saga to complete the Tejada rainbow. I got the base card either in my hobby box or a trade here, then won the Red 1/1 shortly after release on eBay. I knew the rest of them would be easy to pick up except for the Red Ice, which I was outbid for a few times. After I finally won one, I quickly grabbed the remaining 5 cards I needed on COMC to finish it off.
2005 Topps Total Steve Karsay/Mike Stanton Printing Plates

Black, Cyan, Magenta, and Yellow 1/1 Printing Plates
Not a "traditional" rainbow, but maybe a little more impressive. I got the first one the year the product released, and then another 2 came up for auction at the same time a year or two later. I had to wait 5+ years for plate #4 to show up for sale, and $20 later I completed my set. Oddly enough I don't own a single one of the back plates from this set.
Richard
2009 Bowman Sterling WBC Relics Miguel Tejada

Regular, Refractor/199, Blue Refractor/125, Gold Refractor/50, Black Refractor/25, and Red Refractor 1/1
I don't usually pick up non-A's Tejada stuff, but when I saw the Blue Refractor version of this card at a show last year I had to have it, because it just looked awesome (the scan doesn't do the Blue, Gold, and Red cards justice, they're beautiful). I picked up the other versions on eBay and COMC, and last week the Red popped up for auction. I put in a high bid (for me) because I really wanted to complete the rainbow, and won it for half of what I was willing to pay: $22 delivered.
2012 Bowman Ted Lilly

Base, Gold, International, Blue/500, Orange/250, Silver Ice, Red Ice/25, Red 1/1
This was almost the reverse of the saga to complete the Tejada rainbow. I got the base card either in my hobby box or a trade here, then won the Red 1/1 shortly after release on eBay. I knew the rest of them would be easy to pick up except for the Red Ice, which I was outbid for a few times. After I finally won one, I quickly grabbed the remaining 5 cards I needed on COMC to finish it off.
2005 Topps Total Steve Karsay/Mike Stanton Printing Plates

Black, Cyan, Magenta, and Yellow 1/1 Printing Plates
Not a "traditional" rainbow, but maybe a little more impressive. I got the first one the year the product released, and then another 2 came up for auction at the same time a year or two later. I had to wait 5+ years for plate #4 to show up for sale, and $20 later I completed my set. Oddly enough I don't own a single one of the back plates from this set.
Richard