Who first - Agent or Publisher?

I'm steeling myself for yet another round of that wonderful literary game 'Hunt The Publishing Contract'. As many of us know, this can be a dastardly tricky task, unless you've been on television for five minutes in which case it appears to suddenly get a lot easier...

It's actually a while since I've done this, and many things have changed in the industry over the past few years. With that in mind, I'm wondering as to what the general opinion is on who to approach first? It always used to be the standard that you generally needed an agent first, and to dare to approach a publisher direct was thought very bold. But is that still the case?

I've read so many differing reports of this in writing magazines, blogs and in the news that I'm really a bit confused. I can imagine that should a publisher actually pick up something I sent them, then finding an agent retrospectively would probably be a lot easier - but of course, it's getting someone to make that move in the first place at the publishing house.

I'd love to hear your thoughts and experiences in this respect, so please feel free to leave me a comment below. I'd really appreciate it!