Races move into and out of the categories in most of the site's updates, which happen more regularly as events (like announced retirements or government shutdowns) dictate. Meaning that if you track the seats over time, you get a decent sense for how the election will shape up.
Below is every update to the Cook ratings that is currently online since last January. The darker the color, the safer the seat for the appropriate party. (With the exception of expected pick-ups; blue blocks in red territory mean the Republicans are likely to grab a seat that was a Democrat's, and vice versa.) The white line delineates the region that is considered "contested" by the site.
First, notice what's happened over the last few updates. The white line showing the contested seats held by Democrats has slid downward as more seats become toss-ups. The number of Republican contested seats flattened out earlier this year and has largely stayed flat. (The drop-off on the Republican rating happened over the month of July. The bars are not scaled by time horizontally.) The big jump on the Republican side late in 2013 was the shutdown, which moved several Republican seats into play (often only temporarily).
As it stands now, if Democrats and Republicans won their toss-ups and the likely/lean seats, Democrats would pick up one Republican seat (CA-31) and the Republicans would pick up three Democratic ones (NY-21, NC-07, and UT-04). (All four of those seats are held by retiring members of the House.) Which is not how Election Day will work. As with Senate races, one party or the other will probably pick up more of the toss-up and leaner districts -- and that party, given the trend Cook has shown over recent updates, will probably be the Republicans.
But that only became clear relatively recently.