'Arena' is free,and is decent enough.
Are There FREE Chess Software for Game Analysis?

Get a good UI like Arena or ScidvsPC, then get Stockfish 5. Stockfish 5 is the world's most powerful engine, and is free and open-source.

I use Stockfish with the Scid vs. PC GUI, recommended by the Chess.com community:
Scid vs. PC: http://scidvspc.sourceforge.net/#toc3
Stockfish: http://stockfishchess.org/download/

Another great alternative is Houdini 1.5, rated 3000, which I'm using, also on the Scid vs. PC platform.

Whooops... just checked it - it's actually rated 3139 nowadays...
Makes it feel a bit better that I lost to it...
Is Houdini free?
And are these good free ones, such as Stockfish 5 and Arena safe (i.e., no malware attached)? And is it ever worth paying for a program?
Thanks guys!!!

Houdini 1.5 is for free. The most up-to-date version is Houdini 4.0, which is rated over 3250 - this one I really can't reasonably hope to beat - at least I would have to concentrate.
About malware - I didn't notice any, and I've been using it for a rather long period already.

And are these good free ones, such as Stockfish 5 and Arena safe (i.e., no malware attached)? And is it ever worth paying for a program?
Stockfish is malware-free, certainly. I can't speak the same of Arena, however, because I haven't used it.

I think Stockfish/Houdini/Arena are safe as long as you get them from the official sites. (Houdini 1.5a is free; Later versions are not free.)
Stockfish - See Post #4.
Houdini 1.5a - http://www.cruxis.com/chess/houdini.htm
Arena - http://www.playwitharena.com/
Houdini 1.5 is for free. The most up-to-date version is Houdini 4.0, which is rated over 3250 - this one I really can't reasonably hope to beat - at least I would have to concentrate.
About malware - I didn't notice any, and I've been using it for a rather long period already.
If forgot to ask last time...what do you mean when you say one of these programs is rated "_____" (some number)?
Like what does 3250 mean? Thanks again! You guys are awesome.

3250 means that it would be way stronger than the world champion - like, beating him 8 or 9 times out of every ten games, and it can hardly hope to beat it, ever.
A hundred points' difference in ratings already means that you're playing at a different level. The world champion is rated over 350 points below 3250. That's huge.

By the way - I saw your own rating right now... I suppose that a player like you doesn't yet need a computer engine to analyze games. The engine will give you moves that you will not understand, most of the time, and you also won't understand its evaluations.
For you, it's much better to read articles and books and watch videos that are intended for beginners and low intermediates, maybe analyze games together with friends who are stronger, or post in forums asking questions about your games.
I'm wondering if there are any free, safe, and quality chess software that can analyze game positions?
If not, what are the good pay programs? Thanks so much!