What do you like best?
Spanning many years as a consultant at many different client sites, I have been able to connect to all different database types (DB2, Oracle, MySQL, SqlServer, etc) using DbVisualizer.
What do you dislike?
From a functionality standpoint, I have no dislikes. The only dislike I can think of is from the licensing standpoint of not having the option to purchase a lifetime license. I don't like having to renew/upgrade my license every major release.
Recommendations to others considering the product
Each database provider (Oracle, DB2, SQL Server, etc) has its own client, but each of them is biased toward their own database (and most will only let you connect to their type of database). If you're looking for a mature, feature-rich, agnostic database client, you should definitely consider DbVisualizer.
What business problems are you solving with the product? What benefits have you realized?
I have used DbVisualizer to connect to- and query multiple database types. I especially like the ability to visually inspect the database structure (table/view relationships in a hierarchical or orthogonal display).