There are many state pay-as-You pensions systems in the world, as well as private accumulative pensions funds. But can You mention the countries, where intermediary - state accumulative investitions funds function?
South Africa: http://www.pensionfundsonline.co.uk/content/country-profiles/south-africa/98
Argentina (some provinces)
China Colombia Brazil Belgium France Germany Greece Ireland Luxemburg
Mexico Portugal Peru Turkey
Korea India Hong Kong, China Indonesia Jordan Malaysia Philippines Spain
Singapore Thailand Chinese Taipei United States (some states’ schemes)
Australia Austria Canada Costa Rica Denmark Finland Iceland Italy Japan Netherlands Norway Sweden Switzerland United States (Federal Workers and some states’ schemes) United Kingdom
Argentina (federal and some provinces) Chile Czech Republic Hungary Poland Uruguay
Do you mean 'state legislated investment funds'? In which case you may mean Austrakua, where we have what is referred to as Superannuation. Between 7 and 16% of wages are paid into funds by employees, and exchanged for pensions on returner net. The higher the contribution, the lower the state pension, offset through 'super' savings.
One has to be a bit more precise in answering this question. There is number of countries which made savings in privately managed individual accounts mandatory (that is defined contribution advanced funded schemes), many of those listed by Rafik. There are countries where such schemes are not mandated but in practice, through collective agreements, cover majority (like Netherlands). There are also countries which have defined benefit schemes but maintain relatively large reserves - like US, Canada, Sweden, number of African schemes. I don't think there are many countries which have publicly managed individual accounts schemes - most of these are rather of the NDC types (even if some formally are called pension funds), there are individual accounts but included only entitlements on paper, there is no real reserve backing it. Some of these are results of luckily failed privatization reforms - like in Russia or Kazakhstan.