Is It Ok to Slide into First Base?

The answer is yes, but most of the time runners who slide into first base do it for the wrong reason.  By sliding, usually head first, most are of the mind set that they will reach first base more quickly than if they ran through the bag.  Check out the following video clip to see whether or not this is actually true.
Sports Science: Dive vs Run

With the first baseman's foot on the bag, this would not
be the correct time to dive into first base.

I'm sure there are experts out there who would question the science behind the experiment shown in the clip but I think it's pretty clear that a strong case can be made that sliding into first base doesn't benefit you if you are doing it to get to the bag more quickly.  So why do even major leaguers sometimes do it?  "The heat of the moment" is usually the answer.  
When a runner is flying down the line and really needs to be safe, sometimes the competitive nature comes out and the runner just does it.  He doesn't even think about it beforehand.  He just dives for the bag.  I just think of the olympics.  If diving worked, every sprinter in the olympics would dive at the finish line.  None do which tells me it must not help a runner.  Otherwise, they would do it.

To avoid a tag, diving into first base would be justified.

So does that mean a runner should never dive into first base?  No.  There are times when it is a smart move by the runner.  Such a play occurs when a first baseman comes off the bag and tries to catch an errant throw and then apply a tag for the out.  To avoid this, here's what the runner focusses on as he runs down to first base.  He pays attention to the first baseman's feet as he runs.  If he sees the first baseman's feet leave the bag in order to get a throw that seems to be wide on the home plate side of the bag, the runner can try to slide or dive making it harder for the first baseman to tag him.  If the first baseman's feet are on the bag, the runner just continues to run through first base as normal.  
Of course, in many instances, the timing of the play will not give the runner much time, if any, to recognize what's happening and decide to slide.  It should also be noted that many finger, wrist, and shoulder injuries occur when runners dive into first base so it should only be used when completely necessary.