The National Electrical Code still allows for those older homes to retain the 2-wire system because it is not inherently unsafe. What happened is that technology advanced and the 3-wire system is regarded as ‘more’ safe.
If you are purchasing a home with the 2-wire system you need to talk to your home inspector because you can overreact or underreact to this issue.
Rewiring the home is very expensive ($15,000 to $25,000 depending on the size of the home) and sellers are reluctant to do this work for a buyer when the National Electrical Code does not require it.
However, at minimum, your home inspector will likely require or recommend GFCI receptacles to be installed to protect those ungrounded receptacles. This is an approved N.E.C. upgrade to enable you to plug in 3-pin appliances and other equipment.
The GFCI is also a life-saving device that protects you in the event of electricity finding its way to the ground through an appliance, water or human path.
A licensed electrician will know which receptacles at minimum require the GFCI to protect the various circuits in the home. Also, a sticker must be affixed to the GFCI outlet stating ‘No Equipment Ground’. Note also that some modern power strips will not function without a proper ground so computers may not work on older 2-wire systems.
Most all lenders will finance homes with a 2-wire system because they met code at the time of construction. The only issue that might disrupt the financing is if the Appraiser calls it out on his report as a Health and Safety item, or if a Home Inspection Report provided to the Lender calls it a Health and Safety item. Most Appraisers and Home Inspectors that I know will not designate the 2-wire system as a healthy and safety issue.
While this analogy may be simplistic, houses used to be constructed with 2×4 walls but now 2×6 walls are known to provide better structural integrity and provide a better insulation opportunity. A 3-wire house is, similarly, better than a 2-wire house and likely will cost more money to buy, but a 2-wire house, many which have been occupied safely for 60 to 70 years, should not necessarily deter you from your purchasing decision.