In Yugioh can you activate a monster card's effect on your opponent's turn?

it depends on the effect

Continuous - typically come into play as soon as the monster is successfully Summoned, and don't disappear until the monster is removed from the field or flipped face-down.

Ignition - require a manual activation by the card's controller during their Main Phase 1 or 2

Trigger - activate whenever a certain condition on the Field, the nature of play, or the progress of the turn, is met.

Flip - occur when a Flip Effect Monster is flipped face-up; either as a result of battle, a Flip Summon, or by another card effect, such as "Swords of Revealing Light

Quick - (previously known as Multi-Trigger Effects) can be activated either during your turn, or your opponent's turn. They are the only Monster Effects that are Spell Speed 2

*Can you activate a card like Dragunity Legionnaire's effect on your opponent's turn?

no

here's the link

about monster effects

http://yugioh.wikia.com/wiki/Monster_Effect

No. Snipe Hunter and Breaker's effects are called "Ignition effects". Basically an Ignition effect is and effect you choose to activate. You can only activate these during your Main Phase 1 or Main Phase 2. There are some monsters that let you use it's effect on your opponent's turn. These cards will specifiy it on the card.

This Site Might Help You.

RE:

In Yugioh can you activate a monster card's effect on your opponent's turn?

It depends on what kind of effect it is (trigger,continuous, etc.) and also when it can be activated. most cards will say when a monster is allowed to use its effect during your opponents turn. If you want card rulings, Yu-gi-oh! Wikia is a great place to solve Any questions you might have, such as this one.

sorry if this wasnt what you were looking for, but i couldnt give you much information with such a narrow question.

Good luck! ^_^

If a card either (A) activates when a certain condition is fulfilled (Trigger and Flip Effects), (B) outright states on the card that it can be activated during the opponent's turn (Quick Effect), or (C) has an effect that must be Spell Speed 2 to exist but doesn't specifically state that it can't be used during the opponent's turn, it can be used during the opponent's turn (Quick Effects and some Trigger Effects). Continuous Effect monster's effect are always present. If your monster doesn't fall into any of these categories, its effect can only be activated during your turn, during your Main Phases. (There are a few exceptions, like Necro Gardna, but most of them are obvious. As for Necro Gardna, it doesn't make sense for a monster that negates an opponent's monster's attack to not be able to activate on your opponent's turn)

Examples:

Trigger Effect monsters:

- Sangan

- Cyber Valley (effect to negate an attack. This is not a Quick Effect because attack declarations cannot be Chained to, so this effect does not need to be Spell Speed 2)

- Caius, the Shadow Monarch (and yes, there is t least one card that allows you to Normal Summon on your opponent's turn.

Flip Effect monsters:

- Ryko, Lightsworn Hunter

- Penguin Soldier

- Morphing Jar

Type-B Quick Effect monsters:

- Effect Veiler

- Formula Synchron (the Synchro Summon during the opponent's Main Phase)

- Mist Valley Thunder Lord

Type-C More Quick Effect monsters.

- Legendary Six Samurai - Shi En (the negation effect. Since you cannot negate the activation of a card without Chaining to it, the effect must be Spell Speed 2, and Spell Speed 2 cards and effects can be activated during either player's turn, unless they say otherwise. Compare to Chevalier de Fleur who has a similar effect, but has a restriction of only being able to activate during your turn. Chevalier still has a Quick Effect, it just cannot be activated during the opponent's turn.)

- Naturia Beast/Barkion.Landoise (again, the negation effect. Most of these kinds of Quick Effects are negation effects)

- Prime Material Dragon (once again, the negation effect)

EDIT: If someone tries to tell you "if an effect says 'Once per turn' it's an Ignition Effect", don't listen to them because they don't know what they're talking about. In fact, Mist Valley Thunder Lord, the Quick Effect I listed, specifically says "Once per turn" and "This effect can be used during either player's turn." Legendary Six Samurai - Shi En also says once per turn, but can't be an Ignition Effect, because Ignition effects can never Chain to anything to negate their activation. Simplification is one of the worst things people can do in this game, and causes so many misunderstandings. It generally serves to do nothing but teach people lies, like that "Once per turn" effects are Ignition Effects, or that "monsters have priority."

If a monsters effect says "you can only activate this once per turn" it is an ignition effect and you can only activate ignition effects on your turn.

Only if the monsters effect says you can. It has to say "This effect can be used during either players turn" in the effect, such as Junk Gardna

it depends on monster effect...some monsters can be activated only in your turn and others are in both turns..

depends on the monster effect

Only if it states that it can be used on the oppenents turn, otherwises it can only be used on your turn. If it says once per turn it can only be used on your turn, I think.