Its quite common for House members to seek either Senate seats or governorships. This year saw 14 House members try to make the leap. In Senate races, 4 Democrats and 2 Republicans mounted campaigns; for governorships, 2 Democrats and 6 Republicans ran. The results:
3 Democratic wins (Cardin-MD, Brown-OH, Sanders-VT)
1 Democratic loss (Ford-TN)
2 Republican losses (Kennedy-MN, Harris-FL)
1 Democratic win (Strickland-OH)
1 Democratic loss (Davis-FL)
2 Republican wins (Otter-ID, Gibbons-NV)
4 Republican losses (Beauprez-CO, Nussle-IA, Green-WI, Istook-OK)
So, Democrats go 4 for 6, Republicans go 2 for 8.
For House members trying to make this jump, their records inevitably come into play. The thousands of votes they cast become parsed (we see the same thing during presidential races--i.e. Kerry) and, for those Republicans running this year, they got linked to an unpopular president. I know this was definately the case in Wisconsin. While the Governor of Wisconsin has little to say about the war in Iraq, the incumbent Jim Doyle quite successfully used the issue to attack Mark Green.