Seeker White Blood Cells

In a Fantastic Voyage, more often than not, the voyagers will have to contend with white blood cells that are instinctively trying to remove them from the bloodstream. (Hey, the white blood cells don't know the voyagers are there to help!) Either the voyagers will meet them head on and attack, or a Chase Scene will ensue. White blood cells usually don't chase pathogens, they just float around and eat any threats that they bump into.

Anime & Manga

 * The orange blobs within the tree in Pokémon: Lucario and The Mystery of Mew are described as its equivalent to white blood cells. They specifically home in on any nearby humans.

Fanfiction

 * VERY squicky example in Thousand Shinji: when Iruel makes his appearance and tries to infect Rei, her body is transformed into a bloated, pus-dripping mass of flesh that is a literal FACTORY of all kinds of nasty viruses purpose-made to kill Iruel's nanites.

Live Action TV

 * In the Doctor Who story "The Invisible Enemy", the Doctor and Leela travel inside the Doctor's body to deal with an alien infection. At one point, they're attacked by white blood cells, but the Doctor uses a nearby nerve cluster to send them a fake message summoning them to a different part of the body. (This wouldn't work in a human body, where white blood cells just wander aimlessly and deal with whatever they happen to come across, but maybe a Time Lord's immune system works differently.)
 * In an episode of the new Outer Limits series, a spaceship crew punches a hole into another dimension, which they assume to be hyperspaceorsubspace. The main character, who is descended from Magical Native Americans, starts to believe that it is actually the bloodstream of the living universe. What they originally thought to be asteroids turn out to have a similar structure to human white blood cells, except they use gravity to kill infection.

Video Games

 * In Mario & Luigi: Bowser's Inside Story, one room inside Bowser features a large worm boss that is eating what appear to be white knights. After you defeat the worm, the knights ambush you and send you falling. It's not explicitly stated that these are white blood cells, but Toadbert's description of their intent matches perfectly.
 * There's also Alpha Kretin, who is by no means a white blood cell, but attacks in the same way, swarming Princess Peach and then taking some kind of monster form after it's spun away by Mario and Luigi. Sadly, it also appears in the Gauntlet.

Western Animation

 * Osmosis Jones anthropomorphisizes white blood cells, giving them names and allowing them to speak and develop friendships with other cells. The white blood cell team is turned into the police, so they get a lot of chase scenes.
 * During the Teen Titans episode "Crash", Cyborg gets infected with a virus, so Gizmo and Beast Boy go micro and fight the virus. One scene shows white blood cells chasing them.
 * During an episode of The Magic School Bus, "Inside Ralphie", the classroom piles into their bus and goes micro to figure out what's making Ralphie get sick. They encounter white blood cells, which identify the bus as a pathogen and start a chase scene. The white blood cells are shown "sniffing" for pathogens, even though they don't have noses.

Truth In Television

 * This video shows a white blood cell chasing a staphylococcus bacterium.