I'm not the biggest fan of memory games, but I find the most common attitude toward them is almost one of contempt. Compared to that, I love memory games. Some memory games exist primarly as a means of leveling the playing field with young children, but many games use it to good effect. Many games use it simply as yet another feature of the game. The most common reaction though seems to be that a memory element somehow diminishes the game. Part of the reason many games are enjoyable is that they act as interesting cognitive exercises; an auction game leads you to think about precise valuation; geometrical games cause you to exercise your spatial reasoning; negotiation games lead you to anticipate other players behavior. Yet, exercising one's memory is somehow a lesser skill. While I'd still rather play games that make for interesting player interaction and a variety of decisions, memory games deserve more respect.
I created a list on the BoardGameGeek of many under-respected memory games. Below are the games that I put on the list as well as those that others suggested that I personally have played and enjoyed.