I'm getting pretty sick of this meme that the title check being run on Stack Overflow (and Super User and Server Fault) is somehow ineffective, obviously broken, etc. etc.
So, I'm going to drop the science hammer on it.
Before we get into the numbers, I'll outline the inspiration and purpose of these title quality checks.
In a nutshell, there are a few phrases ("problem" and "help" being the most obvious) that are really really strong indicators that a post could use some work; so we slap a "no you don't" hurdle in front of users forcing them to rework the titles at least. Titles are really important, both from a "quality of the site" perspective (who wants a homepage full of Help! posts) and from a "getting your question answered" one (if you're hunting for a question to answer, the more detail in a title the better the odds you'll click on it).
To be clear, the desired outcome of the title quality check is to encourage users to add more detail to (and remove useless, low quality indicative, phrases from) their question titles.
I'm looking at the 200 most recently rejected titles that were still eventually posted as questions. Each of these events will be sorted into one of three buckets based on the changes made to the rejected title: actively helpful, benign, and actively harmful.
actively helpful changes are those that result in more detail being added to a question title. This could just be additional technologies being mentioned, or a more thorough re-write (provided it's still the same question, naturally). Examples would be "heap size problem" -> "Android maximum heap size", or "Technology X Question" -> "Technology X Validation".
benign changes are simple deletions of the offending phrase (problem, help, and what have you) or simple substitutions. "Problem with X" -> "Issue with X" or "Heap allocation problem" -> "Can't allocate on heap" would be examples.
actively harmful changes are the "Pr0blems" (or random "s"s, or awkward non-sense that's clearly meant to dodge the filter) that some are insisting happen every time a user trips over this restriction. Also included are "blind idiot deletions", where a user just deletes words until they stumble around the filter, as that's clearly not "trying to make the question better" behavior.
Final outcome?
actively helpful - 37% of all titles gained some detail
benign - 62% of all titles became no worse
actively harmful - 2% (3 total) posts obviously hacked around the filter
We can break down benign even further, into deleted and replaced. Deleted would be posts that removed the offending word (Problem, help, whatever), replaced meaning that something else we don't check for is slapped in there (Issue, confusion, so long winded way of saying Problem, etc.).
Deleting one of these phrases is a net win. They are the salutations of titles, adding nothing. It's not a strong enough win for me to lump them into actively helpful, but it's still a better outcome than posting the original title.
Replacing one of the phrases is a completely wash, GIGO-style. All the filter accomplished in this case is wasting a few moments of someones time (though they arguably deserved it).
Sub outcome?
deleting - 66% of benign modifications removed pointless verbiage
replacing - 33% of benign modifications were just substitutions (though not harmful ones)
Some other quick stats, these 200 posts occurred over a 24 hour and 30 minute period during which 5166 questions were asked (so approximately 4% of all questions tripped this check). Of these 200, there was a single "false positive" (the title really did need "question" in it, in this case); however that post was ultimately deemed off topic and the owner self-deleted it.
Edit
Factoring in reputation, I looked at users > 150 rep. The same ratio holds (76% improved in some way overall; 40% actively helpful, 0% harmful), though our sample size is getting awfully small (43 users). For >2k rep users only 4 posts triggered this, so it's hardly conclusive, but 75% of those were actively helped with the last post being a deletion (so 100% improved in some small way). The theory that reputation indicates title quality is lacking in support, although aforementioned sample size concerns (exacerbated by the rarity of high rep users asking questions) do exist.
tl;dr - the question title check is pretty effective, contrary to what has been asserted (rather blindly) elsewhere. ~78% of all post titles that trip it are improved in at least some small way, 37% in an unambiguous way. "Hacking around" the filter is in fact very very rare.