David Wayne offers an intriguing critique, suggesting that they are often less about giftedness and more about what people like to do:
I have seen it most commonly in people who fancy themselves to have the gift of prophecy. On more than one occasion I have heard such a person say "well, I guess I just don't have the gift of mercy" after they have emotionally run over someone.
On a deeper level most spiritual gift inventories are just spiritualized versions of temperament tests. Actually, in their place I find temperament tests very helpful and recommend them as good helps for people seeking to identify their strengths, weaknesses and best ways of working with others.
If we could leave spiritual gift inventories on that level - as helpful but not determinative, then I would be fine. The trouble is, spiritual gift inventories are often accompanied with teaching that says that each one of us is given one particular gift by God and we must identify it and use it. Thus, spiritual gift inventories rise to the level of "thus saith the Lord." Others are frustrated that they haven't taken an inventory so they don't know how to serve.
As part of the Annual Clergy Assessment process last year with my PPRC, I took a spiritual gift inventory. It said that I had the gift of prophecy. I guarantee you that I do not. But that result had tallied up because I answered questions to the effect that I enjoy examining Christian ethics.
Such inventories often cheapen the truth of spiritual gifts in order to ensure that congregations have "prophets" and "healers". But a prophet is not a person who studies Christian ethics; it is a person who receives direct spiritual instruction from God. The gift of healing is not about having a good bedside manner. It means someone who can lay on hands and instantly reverse medical ailments.
I find that the benefit of spiritual gift inventories is that they get laypeople talking about what they can and should do to in ministry. The potential pitfall that David Wayne correctly points out is that they can become an overly-strict framework for lay ministry.
UPDATE: Jeff the Baptist's assessment:
I've seen these tests become crutches and stumbling blocks to many. Some things are jobs every believer should be able to do, like evangelism. If I had a nickel for everyone who used the excuse "that's not my spiritual gift" to get out of a jobing they don't want, I'd have a healthy donation to the church building fund. As if Christ said "Go forth and make disciples of all nations... unless you're a Servant, you guys just show up at church workdays."
If you want to use these things in your church, just call them what they are, aptitude or personality tests. Explain to people that they can help them figure out their talents so they can use them to better the Kingdom, but that they aren't some sort of definitive source for spiritual insight and they don't absolve them of spiritual responsibility.