No, labor unions are not a "purely American invention", other countries have them as well: Germany has unions since 1849.
There are, as with all things in life, good times and bad times - but in general, I'd say that unions and managements tend to work together quite well here: yes, negotiations usually start out with unions demanding at least 5% wage increase, a cut in working hours (or at least no increase) and a contract securing all jobs for at least 10 years, while managements usually starts out with a wage freeze, an increase in working hours back to 40 hours (something which a lot of people already, again, have) and no job guarantees at all.
Usually, they end up somewhere in the middle regarding the wages, job guarantees usually end up as 5-10 year guarantees dependant on economic factors and not with a guarantee of employing x number of people at the end of the contract (meaning that people would have to be hired when others leave), but with a guarantee for those who are in the company and who don't leave themselves, don't retire and don't get fired for other reasons (obviously, if you're incompetent then you can still get fired even though you have a "job guarantee").
All in all, I think the system works quite well here - I'm no friend of unions, and I wouldn't join them for anything at the moment, but I do think that the employee's side is better off having them.
Regards (and a Happy New Year),
Smile - it confuses people!