I like new but broken in strings for acoustic recording.  They're usually about where I want them after 30 minutes of playing, give or take.  And that will work for a few days, for me.  
 
Electric dirty guitar, prefer them to be a lot more broken in.  
 
Brand new strings sound cool, but they almost have this "chorus" effect to them, since they sing and respond so much brighter, but that's so limited that you'd have to play your song perfectly to maintain that sound all the way through the song, else you're re-stringing again.  I don't play that perfectly, and it will be hours if not days before I'm done.  
 
But this almost never happens because I don't have the determination to plan and have strings on hand.  Typically, all songs are recorded with old, broken in strings.  sigh...

Thanks for all the input!

New strings will obviously have a brighter sound. The older they get, the more dull the sound becomes.
 
If you're recording clean stuff, like jazz or clean twangy country, you would want to use new strings for the brightness that they impart.  Distorted stuff, I don;t think it really matters as much.
 
When I played live.... lots of gigging, I would change the strings every 2 weeks.  Ernie Ball Super Slinky 009 simply because I didn't want a string breakage in the middle of the show.
 
Also, regarding changing strings.... I read in Guitar Player Magazine many years ago that the Nashville session acoustic players used really heavy gauge strings and on a big country star recording session, they would change the strings after 15 to 20 minutes of playing time. They wanted that super bright overtone that the brand new strings gave them and swore that the strings lost those highlights after a few minutes of playing.  All I know is that those sessions have some amazing sounding acoustic guitar tone.
 
Currently, I change strings only when one of them breaks. So they are all well past a year old.... I will change the strings on my Taylor Acoustic when I have need to record something with it.  Besides.... man, who doesn't love the sound of a guitar with brand new barely broken in strings on it?

I've known jazz electric guitarists of the Joe Pass school who like really worn-in, dull flatwounds. They can help get that very bell-like mostly mids kind of tone, or so they've told me.

For Django style acoustic playing the strings to use are the ones he and his contemporaries used. Savarez Argentines, which are light strings with an unusual wrap and plating. They can be hard to get hold of, but nothing else sounds quite like them, certainly not the nickel-wound strings sold by some manufacturers as "Gypsy Jazz" sets. The closest alternative I've found is a bright electric string of the same guage.

tlw
I've known jazz electric guitarists of the Joe Pass school who like really worn-in, dull flatwounds. They can help get that very bell-like mostly mids kind of tone, or so they've told me.

 
Yes you are correct. I've known several folks who preferred the mellow sound of the worn out nearly dead strings.
 
Essentially what it comes down to is personal likes.  What sounds best to you for the situation.  There's reason to use new bright strings and reason to use old worn out sounding strings.
 
My biggest concern with old strings is that they are grooved, from the frets, and weakened from the acids in sweat, and thus more likely to break in the middle of something important.
 
I've also noticed that the intonation of the instrument goes off a bit as the strings wear out and get grooves in their undersides. The mass of the string changes as a result.

When recording myself or my friends on acoustic guitar (I'm a finger picker), I really dislike brand new strings, nothing but squeak, squeak, ad nauseum, pretty much guaranteeing a long session with Izotope Rx.
 
I know many people will say technique should overcome the squeak, use different fingering, etc. But I work long and hard days finding the perfect voicing for solo song passages to perfectly complement the vocals, so I keep my fingering and trade off with well played strings a week or so old.
 
If I'm just performing rhythm to be panned in with the cymbals and a band or such, maybe a brighter sound played with a pick is what I'll use but...
 
I only listen to classical music these days and for most of the past decade, I was surprised to hear a guitar virtuoso on PBS radio the other day as nothing but squeak, squeak...even at 50 mph on a horrible bumpy road (classic Madison roadway). I thought those cats only used nylon strings but this went on for most of the 5 minute performance to resounding applause at the end.

Guitarhacker
My biggest concern with old strings is that they are grooved, from the frets, and weakened from the acids in sweat, and thus more likely to break in the middle of something important.
 
I've also noticed that the intonation of the instrument goes off a bit as the strings wear out and get grooves in their undersides. The mass of the string changes as a result.

I agree. Though by the time a string has noticable grooves in it, it's usually gone well past "dull" and is fit only for recycling. Strings that worn out won't hold tuning properly either, because they're no longer a uniform diameter and have been stretched for so long the steel core starts to go a bit plastic with fatigue and won't hold a constant tension. At least, that's what seems to happen. The intonation problem isn't just down to lost string mass either, if you measure the pitch of a string in that condition at any given fret it's likely to give a different pitch every time it's played. The string seems to vibrate differently, kind of in sections rather than as a single length.

Badly corroded and worn strings also make excellent files, which is bad news for frets and fingerboard.

robbyk
I only listen to classical music these days and for most of the past decade, I was surprised to hear a guitar virtuoso on PBS radio the other day as nothing but squeak, squeak...even at 50 mph on a horrible bumpy road (classic Madison roadway). I thought those cats only used nylon strings but this went on for most of the 5 minute performance to resounding applause at the end.

The wrap on nylon/synthetic strings can squeak just as much as any other coil-wrapped string.

A high action can be a contributing factor, and many classical guitars have a fairly high action which is exacerbated by the flat or almost flat fingerboard. There's obviously a connection with technique involved somewhere as well.

Then microphones and piezo saddles sometimes seem to really emphasise string and finger noise as well. If the broadcaster adds some compression into the mix (which the audience in the venue probably wouldn't get the 'benefit' of) that obviously makes the problem even worse.

And some people just seem to be squeaky by nature.

tlw, those are all excellent points!