If it's a .zip, then all (reasonably extant versions of) Windows
should have been able to handle it without WinRar, WinZip or any other third-party compressor/decompressor program.
.rar files do need something 3rd party, I think still, but not tried them on Win8, nor possibly Win7, so that may have changed, but WinRar is generally the way round it, and whether the installation 'grabs' .zip and all the other compressed file-types depends on the installer itself, and possibly whether you chose a Custom install. It's different on non-Windows systems, but that way lies madness of waffle, in the absence of further information, so I'll assume we don't need to discuss that, right now.
However, that slight pedantry aside, I suspect that whatever the format you downloaded it
wasn't a supported extension (maybe a .rar, without WinRar installed?), and as Adobe Reader is alphabetically pretty much guaranteed near the top of any list of "suggested programs to use" that your particular flavour of Windows, probably the first time you tried to open the unknown-extensioned file you (deliberately or otherwise) took Adobe as the thing to open it with and did not untick the "always use this program" option (or equivalent).
What Rydel gives as the solution will work, but personally I'd either go into the registry or your Windows version's equivalent of "Folder Options | File Types", find the registered file type involved[1] and remove the erroneous entry (and any others that I would know had been badly assigned, if I had the time and patience), just to keep things neat.
Then work out what program to use and proceed accordingly. More effort needed, but that's my approach. Installing the 'correct' program should work, but some of them are actually friendly enough
not to grab their own extensions unconditionally if they're already grabbed by something else. (Perhaps the best middle-ground is as is done by the ones which add "Open with <foo>" to the context menu, but would leave existing default "Open" and other "Open with..."s. Still needs you to meddle, perhaps redo the default and shuffle the context menu around under the given File Type advanced options.)
If you're not confident with editing the registry then avoid doing that, of course. Less damaging (but you can still disassociate the wrong things if not careful) is the Tools|File Types editor, but this tends to differ more in look and feel, on each subsequent version of Windows, than regedit does, so you might get lost or slightly unsure if you're trying to follow my XP-inspired descriptions.
Sorry, that was longer than intended. Still, hope it helps and doesn't confuse too much. Nor that some other pedant can find
too much wrong with my attempt at an abbreviated summary.
(However, if anyone
does see a problem, please do follow-up. I'm not too proud to be corrected on such matters!)
Ah, Ninjaed by yourself. Asking about WinRAR? Wouldn't know. I don't use it. Except that on every (legit!) installer that I know, any attempt to install toolbars (usually just one at a time)
should be accompanied by a "Do not install toolbars" option (although that's usually ticked by default
(edit: or, rather "Install toolbars" is ticked by default! You'd have to untick that...), for obvious business reasons on behalf of the package supplier). If you're not getting that, or indeed if you
are getting five toolbars at once, then I would instinctively mistrust the installer you have. ICBW, and it could just be agressive.
If you're getting toolbars added from the
website you're getting it from, then I'd avoid that website. Or try to differentiate from the "Download the package you want" button and the "Download something that will perhaps help you download what you want" button, which some websites seem to have, as slight camouflage for their own version of pesterware (or, again, something 3d-party that they're on commission with). Horrible practice, but I can see why they do it, and many other similar things with similar degrees of subterfuge.
However, do you want to tell us
if it's a .rar file you have? Might help solidify whether WinRar is what you need.
[1] You may or may not know this, if "Tools | Folder Options | View | Advanced Settings" (or the equivalent, for your version of Windows/explorer) has "Hide extensions for known file types" set. Being now associated, a ".rnd" random extension will now not show up and you might have to go into properties, or trace what file type(s) are called "<Foo> document" or "<Bar> file" in Details view...