I've always been in the "black ink is boring" camp. I do have a black rollerball that I keep at my work desk and use regularly, but I also have a blue rollerball there. But between black ink and blue ink, I'll take blue 9 times out of 10, regardless of the type of pen.
With fountain pens, for more formal stuff, I usually default to Waterman Serenity Blue. Not only is it a really nice blue with a red sheen on the right paper, it's also just about the most well-behaved ink I've ever used. Even on cheap paper it tends to just work, no fuss. For my own pens, I fill from a bottle, but I also keep cartridges of that ink around to include with fountain pens I gift.
When I'm just writing in my own notebook, or journal, or writing letters, I like to mix it up a lot.
Diamine Blue Velvet is probably my favorite blue. Extremely saturated, cobalt blue that jumps off the page and sheens hard red on good paper, but doesn't look insane or distracting.
Just because I can't have enough blue options, I also keep J. Herbin Eclat de Saphir in the drawer. It's a lighter, less saturated blue. If you're familiar with Dutch ceramics, I chose this ink because it perfectly matches Delft Blue.
Private Reserve Infinity Blue Black is a nice ink when I don't want to go too crazy but still don't want black ink. It's also pH neutral and free of pigments or particulates, so a good choice for my vintage pens that store the ink in latex sacs.
J. Herbin Rouge Grenat is my favorite deep red. It looks like luxury (rather than looking like proofreading).
My EDC frequently has either Monteverde Yosemite Green or Monteverde Citrine in it. Green and burnt orange inks are pretty off-the-wall, but where's the fun in ignoring all the off-the-wall colors available as a fountain pen user?