I recommend Evernote because it matches very well with your specific requirements.
Let's take a look at those requirements:
- When I do research I often find pieces of information (typically between 1-2 sentences) at different locations on the web. I would like be able categorize (or maybe link or tag) these snippets in some kind of searchable database.
Evernote will allow you to quickly save each snippet using the Evernote Web Clipper. Both the Windows and OS X desktop clients will allow you to assign multiple tags to each note.
- The software does not need to be free.
Evernote allows up to 60MB of notes to be stored on their servers for free. After that, you will need to pay. Currently, offline notebooks are very limited in the free version as well.
- However I would prefer it not to be a web-based application (although if you know of some good web-based app for this purpose, I would like to hear about it).
Evernote has dedicated desktop clients as well as a web client. They also have Android and iOS apps. You are free to use whichever combination of products you like to create and access your data.
- Some kind of searchable DB
All text entered in Evernote is fully searchable. With their paid products, you can even search for text within images, as it automatically performs OCR.
In the past, I successfully used Evernote for similar tasks as you are attempting to accomplish. At times, I was frustrated by bugs and functionality limits, but even recalling those issues, I can still recommend it.