Picasa stores tags and captions in it’s own database - the tags are only available within Picasa itself. For application independent tagging of image files, XMP/EXIF/IPTC is what you need. XMP is an XML based tag format for jpeg files. EXIF and IPTC specify data schemas - EXIF stores technical detail about the photo (camera, exposure, lens, time etc) and IPTC can be used to store captions, tags, photographer, etc. The advantage is that you will not lose your tags if you decide to change the application that you use to manage your photos.
IrfanView does IPTC tagging - Google will show up any number of other tools that do the job. I use DigiKam on linux, but plenty of other tools can be used (google IPTC edit).
ETA: I don’t wish to knock Picasa - it’s a pretty good tool. But it’s lack of proper support for a well established standard for Photo metadata is somewhat frustrating to me. It smacks of tie-in, something I really dislike.