No, you can not play World of Warcraft without a subscription unless you play on illegal private servers that are not supported by blizzard. These servers can be much more buggy and you will be kicked off the server many times because the server itself crashes many times and generally by an all around mess.
EDIT: you can now play World of Warcraft for free until level 20.
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This is not possible, as access to the Blizzard servers only is possible with a valid subscription. This needs to be a paid and active subscription connected to a battle.net account. Without this, you cannot play World of Warcraft on official servers.
If you wish to quit playing World of Warcraft, simply enter your battle.net account and stop the subscription payments. Your account will close once the timer expires. This does not delete your account, but you won't be able to play. To delete the account entirely, you can find the option in your account, or by contacting customer support.
There are three subscription plans available: month to month costs 12.99€/£8.99, 3-month subscription costs are 11.99€/£8.39 per month, and six month subscription costs are 10.99€/£7.69 per month.
It does now, it has a kind of subscription option that is the full game, without that it's just way too limited.
The subscription for a 6 month plan is $12.99 per month, or $77.94. The fee must be paid in full.