Note: The information in this post applies to WordPress 2.7 to 3.1. Starting with WordPress 3.2, the memory limit will be configurable again.
WordPress officially needs 256 Megabyte of Memory. Even this is quite a high value, this is not announced in the minimum requirements (some parts of the software like fallback unzip libraries are needing this limit even since the 2.7 version).
Because raising the memory limit over your servers allowance can crash your blog on some servers, it’s adviseable previous to upgrade, check how much memory your server allows. If it’s below 256 Megabytes this could render your blog useless after upgrade.
Related Ticket: #13847
hakre on wordpress 
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the problem is that no shared host will allow 256MB, most are limited to 32-127MB. I think (not being a developer) that the WP devs should come up with methods to reduce the memory load, otherwise the success of WP3 might be hindered.
One solution might be to limit the memory to the memory limit (isn’t it for what its for? 🙂 ). Can be done via a hook even these days. I wonder as well, why they don’t hard-limit it to the servers defaults. I might write a plugin for that at the weekend. Really many users have a problem with this unsafe 256MB guess.
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