Random dice tipping

Ruby, 44

c=0;10.times{$><<c=([*1..6]-[c,7-c]).sample}

I found the [*1..6] trick by lucky experimenting.

GolfScript, 26 chars

0{(.6,5@--\-.,rand=).}10*;

A slight more compressed version of Joey's, basically working around the issue with zero-indexing.

JavaScript (71 characters)

You may need to replace print with alert or something else, depending on your JavaScript environment.

for(C=L=T=0;C++<10;print(L=T))while(!(T-L&&T+L-7))T=Math.random()*6+1|0