It depends on what you define as probiotics. If you are referring to the "food products mega-corporations" as you call them, the answer is most likely No, and arguments are given below. This does not mean that there are no real probiotics which have an actual effect on specific health issues. The answer of mmr gives a few examples.
But again to the claims of these mega-corporations: the European Food Safety authority has researched 800 health claims of such companies, and they could not find relationships.
If you prefer easy reading you may like the article
Probiotic drinks do not aid health, Europe says:
Products such as Yakult, which are sold at a premium over standard
yogurts, cannot be proved to either boost the immune system or aid
digestive health, it has been ruled.
The European Food Safety Authority (EFSA) has examined more than 800
health claims from food companies, including those submitted by the
multi-billion pound probiotic industry.
EFSA's independent panel of scientists found that the claims that
these products could strengthen the body's defences, improve immune
function and reduce gut problems were either so general as to be
inadmissible, or could not be shown to have the claimed effect.
In a separate ruling, the panel examined a dossier of 12 studies
submitted by Yakult for its own strain of probiotic bacteria,
Lactobacillus casei shirota. It found that all were inadequate to
support the company's claim that its products maintained immune
defences against the common cold.
EFSA's ruling is being challenged by the industry, but if these
appeals fail the companies will no longer be allowed to market the
foods as aiding digestion or helping the immune system in future.
More info on the EFSA's own site.
Excerpts from the conclusions:
Claim: “Healthy and balanced digestive system” (ID 1371, 4228)
The claimed effects are “intestinal flora”, “digestive health” and “ingestion of cheese
containing probiotic culture Lb. paracasei NFBC 338 positively influences the healthy balance
of the gut microflora”. The target population is assumed to be the general population. In the
context of the proposed wording, it is assumed that the claimed effects refer to maintenance or
contribution to a healthy and balanced digestive system.
The claimed effects are general and non-specific and do not refer to any specific health claim
as required by Regulation (EC) No 1924/2006.
Claim: Increasing numbers of gastro-intestinal microorganisms (ID 864, 1371, 3073, 4228)
The claimed effects are “gut health”, “intestinal flora”, “digestive health” and “ingestion of
cheese containing probiotic culture Lb. paracasei NFBC 338 positively influences the healthy
balance of the gut microflora”. The target population is assumed to be the general population.
The evidence provided does not establish that increasing numbers of gastro-intestinal
microorganisms is a beneficial physiological effect. A cause and effect relationship has not been established between the consumption of the food(s)/food constituent(s) evaluated in this opinion and a beneficial physiological effect related to increasing numbers of gastro-intestinal microorganisms.
Claim: Decreasing potentially pathogenic gastro-intestinal microorganisms (ID 864, 1371, 3073, 4228)
The claimed effects are “gut health”, “intestinal flora”, “digestive health” and “ingestion of
cheese containing probiotic culture Lb. paracasei NFBC 338 positively influences the healthy
balance of the gut microflora”. The target population is assumed to be the general population.
Decreasing potentially pathogenic gastro-intestinal microorganisms might be a beneficial
physiological effect.
A cause and effect relationship has not been established between the consumption of the
food(s)/food constituent(s) evaluated in this opinion and decreasing potentially pathogenic
gastro-intestinal microorganisms.