If you want to access the web from your Amiga and you have another PC on the network (Mac, Linux, Windows etc.) there are tools that will let a networked Amiga open a web-browser on those machines and display it on the Amiga screen.
With the Amiga hard drives mounted via SAMBA on the host machine (so you can save directly to the Amiga) it looks and feels almost like a native browser only much faster and upto date.
Just google for Amiga & VNC or Remote Desktop.
I have a HP NAS drive (EX470) running Windows Server 2003 which is always on and I click on an icon on the Amiga and a remote FireFox 3.5.6 window opens. Because it is remote everything just works like it would on a PC, Flash, Shockwave, Java etc.
This is going to be one of my next projects. Is a graphics card required in the Amiga to run VNC or Remote Desktop? It would be nice if it was not and was usable on my A1200 w/IndivisionAGA display.
