There are 4 of Tarkovsky's films that have seen Blu-Ray release so far.
Solaris and
Ivan's Childhood have each seen a very good release by criterion. However, his two later (and IMO better) films,
The Sacrifice and
Nostalghia were restored and released by Kino Lorber and they clearly don't have the budget to treat such a restoration properly. Criterion painstakingly removes all scratches, dirt, dust and other junk on the archival film, whereas Kino Lorber does not and it leaves a film image with quite a bit of that static on the screen. Small screen it's not so bad, but anything over 32"/80cm looks pretty rough. It's pretty lame that they bought the rights to these films blu-Ray releases and did such a poor job. I'd love to see Criterion do all of Tarkovsky's films.
Stalker is likely to get a Blu-Ray release in the next year or two. There's a decent DVD version on torrent sites right now, the Artificial Eye release. The best way to see any of Tarkovsky though, is in a repertoire cinema, as his films frequently show up there, and it's a pretty transcendent experience to see his films on that massive screen, especially Stalker and The Sacrifice.
Here's the Artificial Eye version
http://thepiratebay.se//torrent/3897223/Stalker - Andrei Tarkovsky