If you just want a quick and sure way to check your connection to a web server without using a browser, you can use telnet. Here is how:
telnet host_name port
Then you should see output similar to the following
Trying host_name... Connected to host_name. Escape character is '^]'.
Then, you can type the following to retrieve a file in raw ASCII:
GET /index.html HTTP/1.0
For those of you who want to take this further, here is Best Viewed with telnet to port 80 initiative for you.