Can we avoid random chance?

I'm hoping this is already an understood part of "modern" game design, but there are still enough games out there that are using random chance to drift their games into "luck" territory instead of skill.

Some "modern" games that use it quite a bit would be Dominion, Seven Wonders, and Agricola. While these games can all be fun, ultimately it can be very discouraging to know that within the first third of the game you had a disagreeable streak of luck.

Games that have minimized luck lately would be Power Grid, La Havre, and for the most part Small World. To me, these games are much more fun, because losing can often be attributed to something I actually chose. I am the one to blame for the circumstances and I am much happier knowing I can improve.

In general, I think card mechanics should be avoided, as they are great for luck based mechanics and hard to incorporate otherwise. Power Grid does it well be showing in advance what is coming and giving near equal opportunity when powerful options come into play.

How do others feel?