To see most 3D files inc~ .stl files: MeshLabs
To verify 3D Files for printing: NetFabb
TO see and view 3D files for printing: Shapeways
All are free.
You don't have to slice anything, depending on bed size and the item itself.
Whether or not you can print something depends on the bed size, minimum material thicknesses (changes by material and printer) and a whole host of other factors… a definitive answer is impossible without having the files and knowing what printer it is to be printed on and what material that printer will use.
NetFabb will show you any errors and provide some fixes – if it passes netfabb checks then it will be a valid .stl file for printing on *many* systems.
Ditto for Shapeways:
If it passes their checks then it will be good for *many* printers – Shapeways software also tests for material thicknesses and bed size for THEIR materials.
It is a very good baseline if nothing else, and it's entirely free.
An absolute no-brainer for beginners for verifying their .stl files.
Netfabb is all-but an industry standard for validation of 3d files. You will not need the (expensive) paid-for version, just the FREE basic system. It will, initially, probably, blow your mind, persevere with it. It can slice, fill, fix, scale and import/export many different types of files.
If netfabb says your file needs fixing – then it does.
It can then, auto-magically, fix a lot of stuff for you.