(2) I check my field's arXiv every other day or so.
(3) Google Scholar alerts me of papers that it thinks will interest me, based on my own papers, and it's very useful. Most of what it shows me is in fact interesting for me, and it sometimes catches papers from obscure venues that I wouldn't see otherwise. The problem is that you need to have papers published for this to work, and also, it's only good for stuff close to your own work, not that much for expanding horizons - (1), (2) and Google Scholar search are better for that.