Interesting topic! And much more productive than another edition war...
Personally, I go back and forth on the issue. For me, there's an ebb and flow between what's "fantastic" and what's "plausible." So, while I like a cantina of sorts, some things either don't work for me esthetically (and so get changed if they don't fit) or don't work for me conceptually.
Thanks, in large part, to Tolkien, I can easily wrap my brain around a setting with humans, elves, dwarves and halflings. By contrast, in the "real world," we only have one sentient species on this planet - because it out-competed the rest. But I tend to think fantasy entails different assumptions than "the real world" and starts with assumptions more in line with real world myths. Most of those made "the people living over there" into some other race. So, if that's true, I think there's room for plenty of races, and some form of interaction would be "normal." Naturally, some of those interactions will be hostile, and others friendly.
I do still think of humans as the most numerous of the "civilized" races, although representing perhaps a plurality rather than a majority. Moreover, in my campaign, the most recent fallen empire (filling the role Rome did in our middle ages) is almost always one that was human-dominated. That's certainly true in my current 4e setting.
I also tend to think of human settlements as being more "palatable" to different species than those of other races. A dwarf might not find a human village to be ideal, but it's better than an elven one. Similarly, the elf prefers a human village compared to, say, a dwarf one. Therefore, human villages tend to be very Cantina-esque (while still being at least plurality, if not majority, human). Those settlements dominated by other races (which would usually take the form of smaller villages) are generally less cosmopolitan. But that can be true of an isolated human village as well.
Sometimes, I like a race but not its standard description. For example, I think Goliaths are a kick and I even like their back story, but I don't like their look (I feel the same way about Devas - maybe it's the mottled skin tones...). So when they show up in my campaign, they'll look more like firbolgs. The "civilized races" in my current setting include, so far, all the ones from PHB 1&2 (although not all of them have shown up yet). One adventuring group consists of 2 humans, a tiefling, an elf, a winterkin eladrin (on hiatus), and a half-elf (actually half-eladrin, but no mechanical difference other than his "dual heritage" being "human" & "eladrin" rather than "human" & "elf"). The other group is much smaller and includes, at present, a halfling, a human, and an elf.
Personally, I like to cast certain races as antagonists, such as goblins, gnolls, kobolds, orcs, lizard-men, and drow. Yeah, it's cliché, but so what? So I guess I'm not as comfortable with the "wide-open" cantina as some folks. However, I have no problem if a PC wants to be an oddball race. The character in question would just be a rare example of his species.
I haven't decided whether or not to make the Warforged a feature of this campaign setting. No player has expressed an interest, so it hasn't come up yet. Personally, I'm conflicted.