What are all the ways to win by card effect?
What are new ways of winning by card effect?


The following is a list of all the cards that have victory conditions1 for winning that I recall:


Exodia: All five cards in hand and you win. This archetype has several variants, like Exodia Necross. One variant is Exodius the Ultimate Forbidden Lord, which also has victory condition (similar, as you have to send all Exodia pieces to the GY to win).
Destiny Board: All five cards activated on your field, in order, and you win. This is an old set of cards, contemporary of Exodia.
Number 88: Gimmick Puppet of Leo: 3 counters on it and you win. You place them by detaching XYZ material to Leo, which is done by not having Spells or Traps and skipping your Battle phase. Part of the Gimmick Archetype. Its Chaos version, Number C88: Gimmick Puppet Disaster Leo also has win condition, when it has no XYZ material and your Opponent's LP are 2000 or lower.
Ghostrick Angel of Mischief: With 10 XYZ material on it you win. Each turn you can add a Ghostrick card as material to it.
Jackpot 7: All three copies banished by its effect and you win. To banish them your opp has to destroy them while set on your field.
Final Countdown: Just like the song, after 20 turns of its activation you win. Pay 2000 LP to activate. This card was recently limited as some decks were abusing of it.
Vennominaga the Deity of Poisonous Snakes: also 3 venom counters on it and you win. Part of the Venom Archetype.
Holactie the Creator of Light. Remember the Egyptian Gods? Meet their God. Summon it (by tributing the 3 Egyptian Gods) and you win.
Phantasm Spiral Assault: if your Phantasm Spiral Dragon destroys 3 effect monsters while equipped with Phantasm Spiral equip cards you win.


These are only the "legal" or playable cards. For others like the restricted Last Turn and other info about victory conditions and the winning player read here.



1 It is important to stress that conditions are not card effects. Unlike card effects, conditions cannot be negated. This means that Mind Drain can't "negate" Exodia's "effect", as it is a condition. 

This is the same for Number 88; if it has 3 counters you win, period. However, you can cast Breakthrough Skill when Number 88's detach effect is activated, and negate the placement of the counter (ruining his strategy as now it doesn't have enough material to get to 3). But the condition you can't negate.