The Basic Plot of Pokemon
This may seem "innocent," but we need to look at this closer, especially since your children might be playing with fire. Studies have shown that Pokemon and other video games and cartoon shows that portray violence have a negative effect on children . Violence in TV shows, whether it is cartoon or live action violence, is harmful to adults and children, but especially children. Studies have found that violent scenes in children's cartoon shows (such as Pokemon) affect children's thoughts, behaviors, and feelings in the same way that violent TV shows do .
The Spiritual Side of Pokemon
One magical and occultic feature of many Pokemon trading cards is called a "hex move ." A hex move gives the Pokemon creature the ability to place a very harmful spell on its opponent.
The American Heritage College Dictionary dictionary defines a "hex" as "1. An evil spell; a curse ." Merriam-Webster defines a hex as: "to affect as if by an evil spell: jinx"; [or a] "spell, jinx"; [or] "a person who practices witchcraft" . Along with hexes are magical objects (talismans) such as "magic stones" and other occultic objects, which are used to fight off rival Pokemon creatures.
Now, let's look at this from the lens of God's Word, the Bible. In the New Testament book of Acts, we read that people who had used curious arts (or magic / sorcery) burned their books.
Acts 19:19. "Many of them also which used curious arts brought their books together, and burned them before all men: and they counted the price of them, and found it fifty thousand pieces of silver."
Witchcraft and Sorcery are Forbidden in the Scripture.
They counted the cost of being a Christian, and decided it was worth to burn their occult books and follow Jesus. Deuteronomy 18 actually speaks about sorcery and magic.
"9 When thou art come into the land which the Lord thy God giveth thee, thou shalt not learn to do after the abominations of those nations.
10 There shall not be found among you any one that maketh his son or his daughter to pass through the fire, or that useth divination, or an observer of times, or an enchanter, or a witch.
11 Or a charmer, or a consulter with familiar spirits, or a wizard, or a necromancer.
12 For all that do these things are an abomination unto the Lord: and because of these abominations the Lord thy God doth drive them out from before thee."
God forbids witchcraft, sorcery, magic, so-called "psychic powers," astrology, communicating with "spirit guides" (familiar spirits), wizardry, divination, and all forms of occultic power. These are abominations to God. Sorcery and witchcraft are forbidden in the New Testament books too. Galatians 5 speaks of how those who practice witchcraft and idolatry "shall not inherit the kingdom of God."
"19 Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness,
20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,
21 Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God."
God will reward you for your obedience to His Word. You have everything to gain from doing so. But, before you do destroy them, it would be good to let your children know why you must destroy these things. Let them understand how God cannot stand these abominations, and how getting rid of them will be for the better.
Having a Close Walk with God is the Answer.
God breathed His Word for our edification and growth. Listen to what 1 John 1 says about fellowship with God and walking in the light.
1 John 1:5-10
"5 This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all.
6 If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth:
7 But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
8 If we say that we have no sin, we deceive ourselves, and the truth is not in us.
9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
10 If we say that we have not sinned, we make him a liar, and his word is not in us."
I encourage you to seek God about what He wants you to know regarding the cartoon shows you let your kids watch, the books you read, the movies you see, etc. God's best will is always best. He desires for our joy to be full. It cannot be full if we are walking away from God's ways and God's Word.
1 John 1:3-4
"3 That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ.
4 And these things write we unto you, that your joy may be full."
May God bless you and lead you into the truth as you seek to know Him, or know Him better.
If you are coming here as a non-Christian, I encourage you to read this. God desires to have fellowship with you, as you make Jesus Christ your Lord and Savior.
 Lien, Tracy. "How successful is Pokémon?" polygon.com. (2014)
 Siegal, Jacob. "Four out of five ‘Pokemon Go’ users have quit." bgr.com.
 "Pokémon (TV Series 1997– ) - Plot Summary." imdb.com.
 Moore, Matthew. "Pokemon: Cartoons like Pokemon 'can make children aggressive.'" thetelegraph.co.uk. (2009)
 "Focus Blast (Move)." bulbapedia.bulbagarden.net.
 "Hex (move)." pokemondb.net.
 American Heritage College Dictionary. Fourth Edition. Houghton Mifflin Company. (2004)
 "Hex." merriam-webster.com.
 "EP241." bulbapedia.bulbagarden.net.