adapter replacement for 12V 0.5A
Usually, yes. 

There are a couple of things that you need to look out for.

1) Does the connector match up?  Both the size and polarity matter here.

2) Is your new power adapter a SMPS unit or just a plain-old iron-core unit?  The difference is that the SMPS version has a regulated output whereas the iron-core unit will often have an output voltage that is significantly higher than the nameplate rating when used at lower than full output current.

You can usually tell them apart just from the size and weight.  A iron-core power adapter weighs 4 or 5 times as much as the newer SMPS version.