Is it possible to save a Type (using “typeof()”) in an enum?

You can’t do it as the value of an enum, but you could specify it in an attribute:

using System;
using System.Runtime.CompilerServices;

[AttributeUsage(AttributeTargets.Field)]
public class EffectTypeAttribute : Attribute
{
    public Type Type { get; private set; }

    public EffectTypeAttribute(Type type)
    {
        this.Type = type;
    }
}

public class LightningPowerup {}
public class FirePowerup {}
public class WaterPowerup {}

public enum PowerupEffectType
{
    [EffectType(typeof(LightningPowerup))]
    Lightning,
    [EffectType(typeof(FirePowerup))]
    Fire,
    [EffectType(typeof(WaterPowerup))]
    Water
}

You can then extract those attribute values at execution time with reflection. However, I would personally just create a dictionary:

private static Dictionary<PowerupEffectType, Type> EffectTypeMapping =
    new Dictionary<PowerupEffectType, Type>
{
    { PowerupEffectType.Lightning, typeof(LightningPowerup) },
    { PowerupEffectType.Fire, typeof(FirePowerup) },
    { PowerupEffectType.Water, typeof(WaterPowerup) }
};

No need for a special attribute, no need to extract the values with fiddly reflection code.