Does the term "populist" have a negative connotation? Whether used on its own or to describe someone . . . .

Populism. It really depends on who’s talking.
You might also want to check some of them out. :)

Populist is usually said in a positive way, such as when it’s attached to Barack Obama or (gulp) Ron Paul.

Unless you’re part of a snobfest. :)

Populist? Is that like a, what does one call it, a “free-soiler”? “Don’t hang the working man on a ‘cross of gold’” and all that rubbish? Peasants against enclosure and whatnot? ::sniff:: I suppose such nonsense is to be expected from that sort. Populist, indeed.

What do you mean, I’m “in the wrong country”?

It depends which party you are in, and which party the populist is in. Generally, if the populist is in your own party, it’s a great thing; however if the populist is in the other party, the term hints of faint derision. Republic populist seems like an oxymoron, and yet, some exist. Go figure.

Not to me.