I do use Swordsmen now. The main factor is time - if you want to go for a quick attack, Swordsmen come a LOT earlier than Pikemen. I've seen an argument in the thread that Civil Service is "just a few techs away" from Iron Working. This is clearly not true. To get to Iron Working, you need to research three technologies. To get to Civil Service - as many as eleven. I don't have the game available right at this moment, but going by the online Civilopedia, the cost of researching Iron Working and its prerequisites is a total of 305 (adjusted for game speed, but that's not important right now). Civil Service itself costs only a little less than that, 275. Combined with all its prerequisites, it totals 1105. That's more than THREE times the amount of science needed for IW. Of course, going the Civil Service route you'll gain science significantly faster, but it will still be much longer than it takes you to get to IW without building a single Library. And you can use that time to build Barracks and perhaps Heroic Epic rather than Libraries and/or National College.
To sum up, by the time you reach units that are ONE point stronger than Swordsmen (hardly enough to make them invincible even if they have the same experience level), you have enough time to research Iron Working and then, for example, Construction (so, Longbowmen) and a few more techs. If you need Swordsmen, then you clearly want to play a military early game. I think the extra time needed to get 200% more science than you needed for IW is plenty to build a bunch of Swordsmen, likely gain a few levels with each, and then some. By the time you get your first Pikeman, you will have had time to do a LOT with your Swordsmen. Even if you play very passively (why would you do that if you go for early Iron Working?), they have a Heroic Epic +15% strength bonus and at least two levels. That's much stronger than a "fresh" Pikeman from a city without even a Barracks.
And that doesn't take into account the fact that researching Mining gives you a production boost, that Iron gives you another small, but potentially significant production bonus (and both are important if you want to go to war - and you need only a Worker for that, so you are free to keep building military units and buildings), that even before you get Swordsmen you get access to Spearmen (and what else will you use for your army before Civil Service? Warriors?).
And the argument that the AI can get Pikeman early... yeah, they can. But if you play on high enough level, they can always get a unit more powerful than yours. If you play on roughly equal footing and the AI gets Pikeman roughly when you get your Swordsmen, then they are so ahead of you that you are boned anyhow.
I honestly don't see a problem with Swordsmen's strength vs Pikemen. They are not designed now to be the best unit until Longswords, granted. But just because Civil Service is roughly in the same part of the tech tree as Iron Working doesn't mean you can get them at a comparable time.
I do agree, however, that revealing Iron at Bronze Working would be a tremendous improvement. But Swordsmen are only useless if you don't intend to use them in the next few dozen turns after they are built. Isn't that true for, I don't know, *every* unit in the game, except maybe nukes and GDRs?
EDIT: and there's of course the upgrade path thing that people have mentioned in the thread. I personally actually like Lancers a lot. But they do come later than Longswords. Besides, if you play a civilization that has a unique Swordsman/Musketman/Rifleman unit, you might want to get an early start on their levelling by building Swordsmen. So, even if the reasoning I explained above doesn't work for you, building Swordsmen is much better for you in the long run (assuming you play a military game) if you play as Rome, Iroquois, Japan, Denmark, America, France, Ethiopia or Sweden. Depending on your playstyle and whether you have nearby Horses, it might be beneficial for you to play Russia or Ottomans (Russia for the production bonus from Iron, Ottomans if you don't want Sipahi). And if you play as Greece, Persia or Celts, you'll probably research Bronze Working anyhow, which means Iron Working is just one tech away.
So, for one reason or another, up to 13 civilizations will either significantly benefit from early Swordsmen or need just one extra tech to research Iron Working anyhow (I might have missed one or two, listing civilizations from memory).
EDIT 2: oh, and if that's not enough, if you go to war REALLY early, and you actually level up a Warrior or two, they upgrade to Swordsmen if you want to keep them alive. So I guess Aztecs could be added to the list of civilizations that want to fight their wars with the Iron Working technological path.