City specialization is still very useful, but I've found that unlike Civ 4, city specialization doesn't come as straightforward and obvious in Civ 5. I find that most of my cities grow very organic and flexible, which is unlike in Civ 4 that "I'm going to make this a GP farm! I'm going to make that a hammer farm!".
The capital may not necessary be the best city, in my last game as Spain, my second city Barcelona was settled next to Great Barrier Reef and practically in the middle of the world (therefore lots of trade), and became the best culture, best economic and second best production city.
In Civ 5, the revelation of new strategic resources over time can bring massive improvements to city production. In my last game, Warsaw (which I conquered in 2000 BC) became from a puppet goldmine to the best production city due to the appearance of iron/coal/oil/etc. around it over time.
Finally, internal trade routes are EXTREMELY useful and can help cities that have potential to become culture/economy/wonder powerhouse but lack the production (or have fantastic production resources around but are in the middle of a desert or tundra) kickstart very fast and turn into workable state. This also means you're not necessary restricted your wonders building to high production cities, nor are your cities which lack in hammers but have extremely good food production impossible to get culture/tourism/great person wonders. In my last game, capital Madrid, despite being on the seashore with NO water resources, and almost no mines around, was still able to get 1/3 of the world wonders of my empire built there thanks to a cargo ship dedicated to ship productions there. BTW, why not solely focus on Barcelona you ask? That's because world religion's 50% tourism bonus is huge and I didn't want to waste it.
The only one thing that may not require city specialization as much is economy, at least early on. Early on cities are better focused on population growth, and external trade routes provide way much more gold anyway, and all the +% gold buildings/policies don't help them at all. However I think it can be interesting to let one city (preferably already have lots of +gold resources nearby, and lots of jungles around) surrounded by mostly trading posts, supporting its growth and production with only internal trade routes. Of course, whether the opportunity cost of using these caravans/cargo ships to trade for cash instead is worth doing so, is another question (and maybe solved with number crunching).