Good points above, and Adam is right, but a couple more things.
Don't add an index for every column either, some people to that, and it's a problem as well.
Also, think about adding multiple columns to an index; you can often improve performance and cover multiple queries like this.
Consider INCLUDEing columns in your index. Not a ton, since you start to slow down the index, but add 1, 2, 3 when it covers a lot of queries, or queries run very often.