I have a chess site at http://tws27.50webs.com/chess/introduction.html which provides an encyclopaedic coverage of some of these gambits. I am also developing a new site at http://tws27.weebly.com (still in its early stages of construction) which aims to produce ChessCafe.com-style articles accompanied by replayable illustrative games, and expect to blog a fair bit about these systems.
Certain Romantic gambits are occasionally seen even at grandmaster level, for instance Nigel Short often uses the Evans Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4), Alexander Morozevich likes the Albin Counter-Gambit (1.d4 d5 2.c4 e5) and the King's Gambit (1.e4 e5 2.f4) is used as an occasional weapon by numerous grandmasters.
On the whole, though, the top GMs have largely abandoned these Romantic openings because defence at the highest levels of chess is very good, combined with deep computer-assisted opening preparation, and thus opponents can navigate their way through the complications and achieve at least equality. Thus, most GMs tend to adopt more positionally sophisticated openings, against which the paths to equality as Black, or a slight advantage as White, are harder to find.
But the overwhelming majority of chess players never reach grandmaster level. The 19th century gambits are an ideal training ground for tactics and the importance of getting your pieces out for beginners and improving players. For players up to and including county standard, who enjoy wild attacking play, these openings can serve as openings for life and provide a lot of fun.