The original release of the game.

Online Content

There was a very short window for Online services for the Dreamcast, where in the case of Sonic Adventure there were different DLC and online leaderboard services.

Downloadable Content

For Downloadable Content users could download different holiday events in 1999.

Holiday Events

Video By SPEEPsHighway shows the Halloween and Christmas events that users could download on their Dreamcast.

Sonic Adventure Y2K Celebration Video By Tsukento

They also included: 

• The US and EU Dreamcast Launch Party Events
• AT&T Events
• Hidekazu Yukawa Quo Event
• Reebok Challenge (PAL)
• Samba Grand Prix Event
• Kadomatsu New Year’s
• Famitsu Magazine Event (JP)

How to access Downloadable Content and Online Services in the modern day

A video by Jon Cartwright from GVG goes into detail about how to access the Downloadable content using DreamPi. Also goes into detail about the different DLC content from both Sonic Adventure 1 and 2 for the Dreamcast.

DreamPi Method

You can download and utilize DreamPi to Download different DLC online.

Setting Up Dream Pi tutorial: https://dreamcastlive.net/dreampi-tutorial/

Dreamshell Method

You can also download the files individually and load them up through the Dreamshell method as well. Here you would use a Dreamshell SD Card reader that would load different files onto your Dreamcast.

Note: Dreamshells are pretty hard to come by now, but you can find some through an eBay search.