A little while ago I played my first game of The Nacho Incident (a game based around smuggling mexican food into Canada and trying to avoid the Mounties) and like many games it had an amusing theme, some interesting mechanics, and way too much luck for my tastes. There were lots of decisions to make and different things to do but in the end they seemed to be completely dominated by rolls of the figurative dice.
As an example, in the game I played our final scores ended up between 65 and 105. There were several turns where I pulled two green cubes out of the bag and another player pulled out a black and a white cube. My turns were then capped at a gain of 3 points and their turns were capped at a gain of 15 points. There really wasn't anything I could possibly do to win once I got 24 points behind even if my opponent was really bad... and she wasn't.
Not that this is a problem in all games; the format matters a lot. In Texas Hold'Em, of which I am an enduring fan, getting dealt a pair of Aces sure does make you win a lot more money than 7-2 offsuit but that is offset by the fact that the hand is very quick. I figure that it is only a couple minutes per hand so the odds have a way of evening themselves out in Hold'Em that they don't in The Nacho Incident. I could in theory play The Nacho Incident hundreds of times to even out the odds and let good players establish winning records but that isn't practical.
I think this illustrates a really important point in game design: highly random games should also be very quick games. This is a good strategy to implement to keep the hardcore gamers happy because they can actually establish a winning record if their skill warrants it and it also means that more casual gamers are going to get some wins in even if they are bad. Quick games also avoid putting people in unwinnable situations that they have to slug through for hours and hours just to let everyone else compete. Le Havre and Agricola are examples of games that do this and the combination of length and 'sitting around losing for 3 hours' means I don't play them much.
In general the longer a game is the harder it is to make because of the greater need for game balance and catch up mechanisms. It is entirely fine that a hand of poker is heinously luck based because you get another hand of poker right away. Board games would probably have a lot more universal appeal like poker does if they could tap into that style of mechanic more effectively.