What do you like best?
DB2 is relatively simple to maintain and performs very well. It provides a wealth of enterprise class features (mirroring, replication, clustering, etc), and I've found the built in troubleshooting/monitoring tools to be quite handy. IBM support for the product has been excellent as well.
What do you dislike?
Worst ODBC drivers I've ever used - and that says something. There are countless variations and packages, each with 32-bit, 64-bit, and multilanguage flavors. It's easiest if you use the GUI-based tools to create the System DSN (using the Windows ODBC interface has never once worked properly for us), but the GUI tools install a small DB instance wherever they're installed. I don't want that on my servers just to get an ODBC connection set up. The lightweight drivers only provide poorly documented CLI tools and store passwords in cleartext ini files.
Recommendations to others considering the product
There are free products that perform just as well and likely have better integration capabilities with 3rd party applications. However, DB2 was the right fit for us because it worked natively with our aging mainframe.
What business problems are you solving with the product? What benefits have you realized?
Our DB2 cluster mirrors our mainframe databases to act as a data repository for all our business-critical applications. Our mainframe is unable to handle the load from external queries, so the DB2 cluster acts as the read/write for all integrations.