Certain bot tasks routinely get denied as either poorly thought out, lacking consensus, or violating some aspect of the bot policy. Here are some examples of such routinely-denied bots. Keep in mind that consensus can change, and it can always create exceptions for particular, well-defined, tasks.
Examples
editBots to automatically spell-check articles
editBots that automatically attempt to fix spelling or grammar mistakes or apply templates such as {{weasel words}}
are routinely denied. There will always be places where non-standard spellings are intended (for example, quotes), and correcting grammar is even harder. Manually-assisted bots are acceptable, so long as they include international spell checking (not only country-specific spell checking) and the operator does in fact examine every proposed edit before allowing the bot to make it.
Statistic-generating bots, which generate statistics on common misspellings, grammar errors, or the like, and maintenance reports that list possible misspellings are welcome. See Wikipedia:Typo Team for existing efforts and a list of existing interactive spell-checking tools.
Bots to create massive lists of stubs
editBots that create stub articles based on database entries are typically denied as poorly thought out. It is not the job of Wikipedia to needlessly duplicate the content of most databases. However, exceptions do exist, provided the database contains high-quality/reliable data, that individual entries are considered notable, and that the number of stubs created can be reasonably reviewed by human editors. If you think your idea qualifies, run it by a WikiProject first (e.g. WikiProject Plants for articles related to cultivars) to gain consensus for the idea.
Bots to make trivial wikicode improvements
editBots that exist solely for the purpose of making the wikicode "prettier" or "more efficient" routinely get denied when the community does not consider the improvement substantial enough to warrant an edit. For example, the MediaWiki software was updated in November 2008 to change the Image: namespace to File: (as it is not only images that are stored there). However, there is no need to update links using Image: en masse, as links using the old namespace will still work (it was retained specifically for backward compatibility). Such a bot would potentially make thousands of essentially pointless edits. However, exceptions exist.
Bots to update edit counts
editBots which keep an updated figure of a user's edit count on-wiki, for use in userboxes and other templates, are denied as they would have to make many edits, use server resources, and encourage editcountitis. Admins can indirectly get an edit count by putting {{adminstats|{{BASEPAGENAME}}|style=User:X!/adminstats2}}
on their userpage. Editors can get their own edit count from their preferences page, and edit counts for other users may be obtained from the MediaWiki API, the Special:CentralAuth special page, or various toolserver tools (some of which are listed at WP:COUNT).
Bots to update listas
parameters
edit
The community is generally against automatically adding the |listas
parameter to WikiProject banners on article talk pages, due to the possibility of error (see also: 1, 2).
Bots to welcome users
editPerhaps the most frequently rejected proposal is a bot which would place {{welcome}} on the talk pages of all new users. Several variations have been proposed, such as only welcoming users who have made an edit, or a certain number of edits, but these requests are still denied. HostBot is an exception. The idea is that a bot welcoming new users is much less personal than being welcomed by a real user. See also Wikipedia:Perennial proposals#Use a bot to welcome new users.