You can use the "Data View" webpart to take data from a database call, then you can edit the XSLT manually to make it look and do whatever you want, within the scope of that data and XSLT capabilities.

Is there a web part that allows me to do the same thing, but with data that is received by a connected webpart source rather than a database set?

For example: I'd like to be able to pull in a Data View webpart that queries a bunch of data and makes it available all over the page. Then, I would like to hide that Data View. Once it is hidden, I'd like to be able to take another customizable webpart and pull a field (or multiple fields if possible) from the Data View webpart via a webpart connection. This would allow me to display various fields in creative formats without having to call the same query multiple times on the same page by different webparts.

Is there an in house webpart that will allow me to do this?