The Bangkok Post News reports on a bus service starting February, 2006 between Ubon Ratchathani, Thailand and Pakse, Laos with four daily trips on 40-seat air-conditioned buses on the 138-km route. The one-way fare will be 200 baht. No mention of duration or how the border crossing will be handled.
The backpacker level alternative is to take a pickup from Warin Chamrab, bus stop #7, the town a couple of km South of the river from Ubon Ratchathani, to Phibun Mangsahan on route 217 (1 hour, 15 baht (?)). This connects to another pickup to the border at Chong Mek, about 1.5 hours. The last connection from the border to Pakse is a pickup that takes about 1 hour. Current prices unknown for these last two segments.
Edited to add: So, after the preceding was written, I took the B200 bus from Thailand to Lao in March, 2006 and returning from Lao to Thailand in April,. 2006.
The bus takes about 3 hours, including border formalities. The bus stops at the border, all the passengers get out, and pass through exit immigration. Then they reboard the bus, cross the border, and get off the bus again. If anyone needs a visa for Lao, they can get it on arrival with one photo and US$30. Each person them passes through immigration. If entering Lao, there's a fee of THB50.
The bus then continues on to the bus terminal in either Pakse or Ubon. It's hard to imagine that the backpacker alternative that I outline above would be the best way to go for anyone needed to go between Ubon and Pakse. I did see some backpackers at the border, but they may not have known about the bus or had other destinations in mind,