Irfanview is fine. My personal choice is XnView. Also free, nicer UI, much more regularly updated, and totally cross-platform (Mac, Win, Linux) with XnView MP. I'm not sure if Irfanview has as nice of a web export dialog as XnView does, you can fine-tune with visual feedback just like Photoshop (better in some ways, more options).
Edit: Just checked, Irfanview's web exporter is a plugin, but works fine. I like Xnview's more for a couple reasons, first it has some important options that are missing from Irfanview's, like removing metadata and optimizing huffman table (though Irfanview likewise has some things Xnview doesn't, mainly a resizable export window and some possibly handy functions like resize and rotate that are built-in to the export dialog, but which Xnview just handles in the main UI, so aren't really necessary). Second, XnView exports to more formats from the Export dialog. Both are good options really, I just think XnView is the better of the two.