I used to read the Grauniad, but its tendency to be biased rather put me off. You can substitute the names of all of the other papers in that sentence and it's still true, which is why I've given up reading the news. You'd think that with them becoming decreasingly relevant they'd actually try for a selling point such as being honest and impartial, but I guess an aversion to those qualities is in most journalists' genes.
The way I see it, The Guardian shows less bias than the average rag, and the fact that it is owned by a trust (which is tasked with keeping the paper independent) makes it a little more trustworthy than, say, Newscorp (which almost definitely takes advantage of its power to influence people). If I may http://www.guardian.co.uk/media/2012/may/17/harold-evans-leveson-murdoch-times a Guardian article...
So, yes, the G may have a bias these days. But at least they still have
some journalistic integrity, and they claim that various things (such as political support) are dictated by internal staff discussions, rather than being passed down from high above

. And I suppose that papers which are idealistic enough to be independent these days are naturally going to have a leftish leaning.
What alternatives are there? I admit that I haven't gone to much effort to look, but good newspapers are increasingly rare. There are a few internet-only news sites, too, but I'm not sure how many of them are good. Blogs provide an alternative, but you have to be even more careful in picking them, since it's quite easy for them to stray into being opinion rather than journalism, and there are plenty out there which end up being part of a self-reinforcing loop -- blog 1 posts something, blog 2 posts something based on blog 1, blog 3 posts something based on blog 2.... then blog 1 posts something based on blog 42...