Hi--sorry I didn't get right back, I'm trying to do several things at once to get ready for a busy weekend at church, and I do have to run very shortly. I don't have time to sit and write something comprehensive, so I'm going to just write out some ideas off the top of my head, and I'm sure others on here will have something to contribute.
Forms for organ music expanded during the Romantic era, just as forms for other instruments and orchestra. As the sonata developed during the Classical era, mostly for piano, some Romantic composers wrote sonatas for organ. Mendelssohn did, though he is transitional and almost more Classical than Romantic. Another really good composer of organ sonatas was Josef Rheinberger, who was influenced by Mendelssohn's work. Some composers continued to write choral preludes, as Brahms did at the end of his life, though Brahms wrote very little for the organ compared to his other music. There was Max Reger, who wrote very expansive chorale based works. In the French school, there was Cesar Franck, who experimented with the more current freer forms, or freer methods of using traditional forms. His Grande Piece Symphonique is cyclical, and it paved the way for the organ symphonies of Charles-Marie Widor, which are sometimes more like suites than like symphonies, as they do not always use traditional forms (sonata form, for example) in their movements. Rheinberger's sonatas are actually more like symphonies in some ways than Widor's symphonies. In America, two of the better Romantic organ composers were Chadwick and Arthur Foote, but there were others as well.
Romantic organ composers continued to attempt to write fugues. Mendelssohn wrote fugues, as did Rheinberger, and Brahms also. An important late French Romantic composer was Marcel Dupre, who wrote Preludes and Fugues as well as more expansive, freer forms, sometimes programmatic. Another such composer (and I'm sure Giovanni would hit me if I forget) was Tournemire, who based some music on Gregorian chant.
This is just a start with the ones that come immediately to my mind. I'm sure we could go on and on with this, and that would be good. Please don't take this as comprehensive, as I'm in a hurry and don't really have time to sit and think about it. Start with a search on the composers I mentioned, and you'll have plenty of material to get you started. Good luck, and let's see if this develops into an interesting thread!