This is an interesting question (I really mean this — see below), for which a straight answer is remarkably difficult to find on the web. When I googled for it I got pages with statements that obligate anaerobic bacteria still had the electron transport chain (ETC) and ATP synthase as there were different electron acceptors other than oxygen. Yes, we know that things are different in thermal vents and hot springs, but what about gas gangrene? I am not a microbiologist, but I did play with the metabolism of some bacteria for a biochemical bioinformatics lab some years ago, so I can give two instances where anaerobic bacteria appear to lack either the ETC or both the ETC and ATP synthase.
This is the anaerobic fermenting bacterium that leads to gas gangrene in infected wounds and was a major cause of limb loss and mortality in the First World War. The DNA sequence of Clostridium perfringens has been determined. I quote at length from the paper as it describes the fermentation, but italicise the key statement for those who wish to skip this:
We could not find any genes coding for tricarboxylic acid (TCA) cycle- or respiratory-chain-related proteins, in contrast to C. acetobutylicum, which has incomplete TCA cycle enzymes. Similar to C. acetobutylicum, we could construct a pathway map for anaerobic fermentation resulting in the production of lactate, alcohol, acetate, and butyrate, all of which have been commonly detected in C. perfringens cultures. In the fermentation pathway, pyruvate is converted into acetyl-CoA by pyruvate-ferredoxin oxidoreductase (CPE2061), producing CO2 gas and reduced ferredoxin. Electrons from the reduced ferredoxin are transferred to protons by hydrogenase (CPE2346), resulting in the formation of hydrogen molecules (H2) that are released from the cell together with CO2.
The related bacterium, Clostridium acetobutylicum, mentioned in the extract, is also an obligate anaerobe. (It ferments a variety of plant mono- and poly-saccharides to acetone, butanol and ethanol — used to produce explosives in the First World War.) Although it has some enzymes of the TCA-cycle, it is unable to use the cycle oxidatively, and, like Clostridium perifringens, lacks the enzymes of the electron transport chain and an ATP synthase.
Ureaplasma urealyticum (Ureaplasma parvum)
This micro-organism is a micoplasma (Mollicute) rather than a bacterium — i.e. it lacks a cell wall. It infects the human urogenital tract. It lacks the components of an electron transport chain but does possess a functional ATP synthase. It generates a hydrogen ion gradient, not by increasing the hydrogen ion concentration within the inter-membrane space by the oxidation of NADH in the ETC, but by reducing the intracellular hydrogen ion concentration by generating ammonia from urea (plentiful in its habitat) in a reaction catalysed by the urease it encodes. The sequence of the organism and references to previous work on its urease activity can be found here.
The reason I find this question interesting is that anaerobic organisms preceded aerobic organisms, so the question arises whether there are any contemporary anaerobic bacteria that have evolved from these primaeval anaerobes and have never possessed an electron transport system — or are all contemporary anaerobic organisms lacking an ETC derived from organisms with an ETC (aerobic or using some other electron acceptor) and have just lost these functions through non-use (as is most likely in the examples above)? This question must surely have been considered by those in the field.