Before knowing which games are good, you need to know what games you like. Here are the categories:

RPG (role-playing-games)

These games have a unique battle style that you can't control 100% of the time, there are enemies from the field that bump into you to start a battle. You gain exp. and level up to get better stats to defeat the finial boss. Most of them have a good plot.

Some RPG games: Pokemon, Mario RPG's, Mother trillogy 

Platformer

In these games, you go on a side-scrolling 2D adventure throughout a world to accomplish the main story.ex. saving the princess.You collect powers up on your way to battle enemies.The battle style is simple, you just use a main attack,ex. jump,burn,freeze,run away. At the end, you just battle a final boss.Not too much of a big plot or story but multiplayer is always fun.

Some Platformer games: Super Mario Bros., Kirby, Donkey Kong 3D.

Adventure

I would say that Adventure is a combination of RPG and Platformer. Like RPG, there is a plot and you walk around the world trying to complete the story. The battle style is like a Platformer. This time, since your on an adventure, you can collect new weapons, skill, attacks to use in the field battle.

Some adventure games: the Legend of Zelda, Super Mario 3D Land/World,  

Fighting

There are a lot of different characters usually with different stats and you go to battle with other characters in the same game and just duke it out and start brawling. Some are simple 1-on-1's and some are complicated with big movesets and items and OMG!(they aren't that hard, just play if you like)

Some Fighting games: Super smash bros 64/Melee/Brawl/4, Punch Out

Personal Games

I don't know that much of a better genre name but personal games are games that let you do your own things however you like. Again, it's personal but some have multiplayer modes. I'm not an expert on this type of games but they do seem really fun.

Some personal games: Animal crossing(all), Tomodachi Life

Spin-Off

These games might be considered weird but what it is is a game from a popular franchise turned into something simple like maybe a dreadful ultimate fighting game and then all the characters come to play sports.

Some spin-offs: Dance Dance Revolution Mario Mix, Pokemon Snap, Freshly-Picked Tingle's Rosy Rupeeland

Sports

This one, well, you should already know what it is, it's sports. Nothing more said.

Some Sport Games: Fifa, Madden, Mario Sports

Party

These games are really fun family games. You party throughout a board trying to accomplish something to win and there are minigames that affect who and how some player would win.These games are really fun so you should go and try some right now

Some Party Games: Mario Party, Wii party, Wii party U