Talking about Europe....
DL requires you to be in K fare or higher to use miles to upgrade, but no co-pay...
Delta
AA allows you to upgrade to business from any fare class, but they require miles+copay... However, their copay is reasonable at $350 from deeply discounted economy fares..
American
Continental also allows upgrades to BF on international flights, however, the copay is higher from deeply discounted fares at $500. At the same time, CO is asking for 20,000 miles vs. 25,000 for AA.
Continental