Typical 4/4 time has the little (I think) has the little "1 cent" symbol that looks like "c", that, or something to that effect.

Now, if I see that symbol, the "c", but with a vertical line through it, what does that mean? I've seen it written before, but through my books I couldn't find it. I'm trying to read some CCR tunes (I know I know, but these guys are good for blues progressions :) ), and a lot of their tunes are in this fashion.

Doesn't this mean 1/2 time? And if so, how do I play that? Faster, slower?

Any help would be very cool.

That's "cut time" or 2/2. It doesn't affect the tempo.

That's it.
The accents or strong beats are the 1 & 3 so it feels like two beats per bar instead of four.

SB
well cut time is two beats per bar...

Yes I know it feels like 2 beats per bar, but you still have four beats written in the bar.
I just wanted to specifie that.
SB
But technically in cut time a half note is one "beat."

I think polkas are written in 2/4...

One thing I think it's important about cut time: The right way of understanding this time signature is like two beats, each one being a half note. That's why the fractionary number for this is 2/2. But I've known people who prefer to think of that as a 4/4 measure at double speed (four beats, each one being a quarter note), which may not be strictly correct, but valid IMO. So many people ask: Why writing a piece in 2/2 instead of 4/4 at double speed? There's a "psychological" reason for that: When you are an experienced player with good reading skills and you're given a sheet written in 2/2 time, the cut time signature automatically "warns" you that the piece you're about to play is something that goes fast. Not necessarily super fast, but fast enough to become counting 1-2-3-4 at double speed (thinking as 4/4) an uncomfortable task. Counting beats the right way in this time signature results in a more relaxed subdivision. Something similar happens with 6/8 time: It can be understood as a 6 beats measure, each one being an 8th note, or as a 2 beat measure, each one being a dotted quarter note. The first way is used in very slow pieces while the second is adequate for faster ones.