I'm a XnView (freeware) fan.
Irfanview's interface looks dated and doesn't get updated very often.
FastStone is popular and it comes down to taste.
I like the reconfigurability (you have preset, reconfigurable hot-keys for just about everything) and the very small size of XnView - easy to run from a USB stick.
You can also operate two independent sets of image selection: Tagged; Selected.
Tagging is when you click the little tick box at the top left of a thumbnail. You also have commands like "Show all (only) tagged files" and "Invert (tagged)".
Selection is the standard Windows file section methods like Ctrl-A, Shift & Ctrl selection modifiers as well as others like Invert Selection.
Say you had 4 files: 1, 2, 3, 4.
You tag 1 & 2.
You select 2, 3, 4.
When you right click and select Copy or Move (or use their hotkeys) you will be asked which set you want to use. (You can also tick a "Don't Ask Again" box). By the way, you can easily set up multiple Favourite directories for browsing & file operation destinations.
Tagging is cleared after an operation - Selection isn't. This can come in handy.
Good handling of file-already-exists situations. Both images are displayed with date, dimensions & file size shown. You can easily set up a rename.
Reconfiguration of panels and their size. Tabs used as well to save screen space.
Batch Processing (can be multi-process).
Batch Rename with drop-down templates, but you can easily amend or add your own.
Continuous frame shooting
Image Compare.
Contact Sheets.
Set up a Web Page (with thumbnails leading to bigger images (a number of different templates provided and others have contributed).
Freeware Photo Web Page Creators
Single or Multiple Screen Grabbing with Cropping.
Freeform & constrained cropped. Constrained by size or AR. Preconfigured ARs. You can also save your own from a current selection as a new "Custom" selection, and then bring it up again with the C hotkey. Handy when you're moving through a set of images and want to use the same crop frame. Switching of W & H with the Tab key i.e. from 640x480 to 480x640 or from 3:2 to 2:3.
Thumbnails: small to very large.
Open with... (Alt-1 to Alt-9 for your configured other raw converters and image editors, F3 for Associated Program, F4 for Associated Editor)
Image adjustment, filters etc.
Batch scripting via modifying, in a text file, options in command boxes.
Tip: XnView output directory relative addressing
You can also filter & sort in lots of ways. I like the different views of the the files when browsing and I've configured both the hover tool-tips & Details, as well as the overlayed Info panel in Image, Fullscreen and Slideshow views, to show EXIF info.
Some different ways to show EXIF exposure info in XnView
You can save different slideshows and and load them from your USB stick - great when you need to take some image to show to your workmates.
To speed up the loading of raw files, configure XnView to use the embedded JPEG preview rather than doing any on-the-fly DCRAW conversion: Tools | Options (or F12) | View | Misc | Camera Raw: Embedded Thumbnail.
The single EXE that does this is 4.3 MB so it loads fast and is easy to carry around. No other DLLs or or other files required. Config settings can be written to either the registry or to a local INI file.
Dan