Cron,
It depends on what you want the web applications to do & what skills you want to pick up & why.
There is a lot of development around on LAMP as suggested by bnt & liftboy above, but if you want to be building skills to use elsewhere then it may be worth looking at
Mono which is an open source implementation of some of the Microsoft stack including ASP.NET. By it's nature it's not the latest & greatest of the .NET stacks, but it is a useful tool if you ever wanted to transfer skills back to the Microsoft world (and it has
VB.NET if you want it, I know you said "Delphi" but...). Mono is a little more difficult to set up on Linux than out of the box LAMP but it's swings & roundabouts.
The other way to look is if you simply want to do pure Web development for your own use, then
Oracle Application Express is available free for personal use but you also have to get their free version of Oracle RDBMS as well. Again they run on Linux but need to be set up. There are quite a few commercial Oracle APEX sites out there so again it's something to think of if you are trying to skills build.
Whatever you do, have fun with it
batninth