[Kryptid (OP)]

If all species of the animal kingdom could be removed from the Earth all at once somehow, which kingdom would be the most likely to step up and evolve to replace their roles in the environment? Fungi? Protists such as slime molds? Even some plants?

Slime molds, since they are already mobile, might have a good head start at replacing animals. Might they evolve to gain more complex anatomy and tissue differentiation? What might these first "neo-animals" look like? Slugs? Might they evolve internal skeletons? Would they even resemble any normal animals?

[CliffordK]

I suppose the question is what a loss of "animals" means.

Animals?
Insects?
Bees?

A lot of plant species would die out without bees.

Nature must have a balance between photosynthesis and decomposers.  Yet, many of the decomposers will function just fine without large animals.  I suppose flies, maggots, worms, & etc are part of the plant decomposition.  But, the lack of these might just slow down the process.

At least initially, bacteria, and fungi would have to maintain the Carbon/CO₂ balance on Earth, without which there would be a mass extinction. 

Over millions or billions of years, any of the Eukaryotes could regain the mobility.  First as insects, with crawling or sliding in the case of slugs coming before flying.  Or, perhaps starting as an aquatic species.  Jelly Fish?

While a photosynthesizing plant might develop the ability to move, it is most likely to start with a type of decomposer, using the abundant plant matter and oxygen as energy sources.

[Nizzle]

The OP says "all species from the Animal Kingdom" so that includes Insects, jelly fish, sponges and even a whole bunch of microscopic organisms..

In other words, if you take the recent Cavalier-Smith classification, you're only left with the other 5 kingdoms: Bacteria, Protozoa, Chromista, Plantae and Fungi.

As CliffordK already suggested, you'll see a strong decline in number of species in other Kingdoms as well (mainly in the plants kingdom, but there are species from the other kingdoms as well that are dependent on Animals).

After this initial massive extinction, you'll see recovery and a vast increase in amounts of species because there will be a huge ecological niche left to be taken over.

Now the question of the OP asks "what would replace the animals" and my guestimate is that evolution will run it's course again and produce similar, but not the same results.

Similar... because the environment will be very similar: Gravity is still 1G, life will still be structured in our rigid DNA-RNA-protein mechanism with 4 nucleotides and ~20 aminoacids, temperature range might differ a few degrees, oxygen concentration might differ some percentages, ...

...but not the same because evolution happens through random mutations, and randomness never produces the same result twice, at least not on the massive scale that is evolution.

Now if you ask for concrete examples, I'm sorry but I'll leave that to your own imagination

[MikeS]

I imagine that if all animal species were removed from the Earth, evolution would soon (relatively speaking) fill the void with new animals.  Animals fill a niche that plants do not, so animals would develop to fill that empty niche.

Body layout is much the same for most creatures on Earth, probably because it is the one that works best.  Therefore it seems probably that evolution would do something very similar again.  Likewise, aliens would also possibly have a similar body plan.

[Nizzle]

Body layout is much the same for most creatures on Earth, probably because it is the one that works best.

Body layout is much the same for most creatures because they had common ancestors. Not necessarily because it works best. Maybe if mammals had to evolve again, they'd all have 6 limbs instead of 4, and 4 eyes instead of 2.

[MikeS]

Whilst there are exceptions to every rule nature does seem to follow the simplest path that works.  Two eyes being the minimum number required for binocular vision and a leg on each corner (4) being the minimum number required to (easily) balance and not fall over.

quote Nizzle
"Body layout is much the same for most creatures because they had common ancestors."

True but these common ancestors were themselves a result of a large amount of experiments by nature into what worked and what didn't.

Even insects share a similar body plan to animals although they diverged a very long time ago.  That is head at one end, bum at the other and gut in between.  The simplest (digestive in this case) path that worked.

[Atomic-S]

We might observe Mars: Although there is no known extant life there at present, the ecological niche seems to be becoming populated with robots.

[Nizzle]

Two eyes being the minimum number required for binocular vision and a leg on each corner (4) being the minimum number required to (easily) balance and not fall over.
...
Even insects share a similar body plan to animals although they diverged a very long time ago.  That is head at one end, bum at the other and gut in between.  The simplest (digestive in this case) path that worked.

Yet insects have 6 legs and mammals 4