There's an interesting poll running right now on Liverpool's official site. The question is asked "Which Trophy Do You Want the Most?" in 2008-09. The Champions League is always hyped as the most prestigious trophy in European club football, but Reds fans apparently don't see it that way.
When I voted around 1:00 pm CT on Wednesday, the Premier League title had 5,890 votes to the Champions League's 435, with less than 100 combined for the FA Cup and Carling Cup. Liverpool's 18 league championships are an English record, but they haven't captured domestic honors since 1990. Since that time Manchester United have won 10 titles to cut Liverpool's lead to 18-17, which goes a long way in explaining the fans' hunger for the Premier League trophy.
I'd like to see the results if the same question were posed to Chelsea fans. I suspect the numbers would be far different.