There are several online Go servers - so you can play Go on the internet anytime with players from around the world. I'm only listing here the ones I used and liked.
For a modern database search engine of pro game patterns, I recommend Waltheri.
Gobase is a website that offers both the database and the searching as an online service. Just follow the "Pattern search" link, then "Enter your repository" and then "Edit board". It will return up to 100 professional games that match the position you entered.
The most popular, freely available computer AI system is KataGo. It can give pro players 3 handicap stones for a balanced game.
I use Drago - very lightweight download, my favourite software for recording and replaying games. I also use it to search game patterns in a game collection.
The best Go encyclopedia I know of is GoGoD. I bought this in 2001 or so (they must have added a lot to it meanwhile), but I was delighted with their articles on Go history, players, events...
While not an encyclopedia in the strict sense, Sensei's Library is a wonderful resource. Use the search field to look up on anything Go related - you'll most of the times find something useful.
Some of the Go servers do live broadcasts on the internet of top professional Go games.
In order to fully enjoy following these matches, I recommend to look up the players' names and career highlights in advance on Sensei's Library to get familiar with them.
The best server I know of for live broadcasts is Cyberoro. Every Thursday in Japan (Wednesday evening in US, midnight in Europe) there are top professional games at the Nihon Ki-in that you can follow live. There are also top pro games from China and Korea very often - but I don't know the schedule.