I swear by the armadillos. I bought a set a for winter riding in early 2002, then kept them on all summer without a single flat. 4500 miles later I noticed some wear and replaced them with a new set, still flatless after a couple thousand miles.
They're very good in wet weather too. The only place I've found them so far has been Toga, but other shops in town must have them.

I personally just buy whatever tires are on sales and put Tuffy strips in them. Only had two flat all last year, and they were due to nail or sidewall punctures. Over a thousand miles this season without a flat, so far. Tuffy strips add a little weight, but if weight is not a consideration, try it.

I agree with Diane about removing glass and debris immediately after you've ridden through rough stuff. But even good eye sight won't always protect you, especially if you ride in the dark.

In London I used to commute on Continental Top Touring tyres, the predecessor to Continental Top Touring 2000. My size was 700x28, I don't think they make them in 700x23, unfortunately.

If you intend to use them for commuting, I think they are hard to beat. Twice I managed to get 10,000 miles out of a back tyre before I had my first puncture. In both cases, after I had fixed it, I got another 4,000 puncture-free miles out of it before I had to replace it. The front tyres can go on for at least 15,000 miles. I thought I had been exceptionally lucky with my first set of Conti Top Touring, but when my second set proved to be just as robust, I assumed it was because they are very good tyres. While London's road surfaces are much better than New York's, they have just as much broken glass, nails etc.

These tyres give good traction in wet and damp weather, which is definitely a regular occurrence when commuting in London. This was an important consideration for me when commuting.

If you really insist on a 700x23, I'm not sure what to recommend. My 700x23 Vredestein Fortezzas are pretty good on my road bike, but I rarely get more than 2,000 miles out of them in total, and I certainly wouldn't use them for everyday commuting. I don't commute these days, as I work from home, so I can't tell you much about the Specialized tyres I have on my touring bike because they've yet to do achieve a high mileage, as most of my riding is on my road bike these days. But the first 1,000 miles have been puncture free. I no longer have the bike with the Contis and my touring bike came with Specialized.

I commute on 700x23 clinchers, and have had good luck with Michelin Eriliums and Continental Ultra Gatorskins. Both have Kevlar belts. Both run at about 100psi. Both stand up well to the tortures of NYC streets. I found the Contis to have tougher treads, but they cost more, and their sidewalls are less rugged. The Michelins have a slight file tread; the Contis have a minimal grooved tread. Both are ok training tires -- not especially light or supple, but an acceptable compromise between ride and durability for everyday use. Either one can get cut up by glass in the rain, but they are bicycle tires... In the dry, it takes something pretty substantial to hole your tube with either. Figure about $26 for the Michelins, closer to $40 for the Continentals.