I've flown from North America to Latvia and back a lot in last 10 years. Typically, it involves flying from Riga to some major North European airport (London, Franfurt, Copenhagen), then, from there to North America. And there might be another change of planes in North America, if the final destination airport does not have direct connections to North Europe. Some of those trips have been quite exhausting for me.
A direct flight from Riga to, say, New York would make things much easier. There was one in early 1990s, thanks to Latvian American businessman Georgs Mikelsons, the founder and CEO of American Trans Air. When Latvia became independent, American Trans Air started a New York-Riga flight (with a stopover in Belfast, Northern Ireland). The flight did not quite fit together with the rest of ATA's flight network, though, and was discontinued a few years later.
Another flight was started in 2005, by Uzbekistan Airways, which chose Riga as a stopover point for their Tashkent-New York flights. I do get a bit nervous about their safety standards, though. (I don't know anything specifically about Uzbekistan Airways but a number of airlines from Russia and CIS have problems in that aspect.) In contrast, I feel perfectly safe flying Air Baltic.
The growth of Riga airport in last years has been extremely impressive. The number of passengers has more than tripled in 4 years and there has been a lot of new flights to new destinations. And direct flights between Latvia and North America no longer look impossible.
UPDATE (31/08): In comments, a reader says:
Hello, my wife flew Uzbek Airlines from New York to Riga and back last year. It was a great experience from start to finish. Due to us having two young boys, it's so much easier to fly non-stop than to have layovers. I've never heard anything about Uzbek Airlines having quality problems.I'm glad to hear that. If I need to travel from Riga to New York, I might try Uzbek Airlines.
UPDATE 2: I am told that Latvians from Latvia are a bit cautious about the Uzbek Airlines flight (in the same way that I was when I wrote this post), while Latvian Americans fly it in large numbers. And their experiences with flying Uzbek Airlines are good.