Players are on 1st & 3rd . ball is pitched ,player on 1st runs to second but catcher doesn't throw it to second. Is this still counted as a stolen base?
In the NCAA, this would depend on the circumstances of the game. If the runner were effectively immaterial to the outcome of the game - either because the winning run is the runner on third, or because more than two runs are needed to tie the game, and it is the bottom of the last inning (seventh or later) - then the stolen base might not be counted due to defensive indifference.
Note that this is up to the official scorer. In cases that are not the final inning, the above scenario (first and third) might be still considered defensive indifference, if the scorer ruled that the catcher held the ball in order to prevent the runner on third from scoring. If they ruled that the base was already clearly stolen (and the lack of throw was due to the unlikelihood of catching the runner) then it should be a stolen base.
From the NCAA Rulebook, rule 14, Official Scorer:
14.2.7 Defensive Indifference: Scoring term to describe the lack of a defensive play on a runner or base runner running the bases after a batted ball, or a base runner attempting to steal a base after a pitch when the player’s advance is perceived to have no bearing on the outcome of the game.
A. R. 184.108.40.206 In the bottom of the seventh inning with no one out and the winning run on third base, the batter taps the ball to the pitcher who makes no throw to first base to prevent the winning run from scoring. RULING—Credit the batter with a fielder’s choice to gain first base and an additional fielder’s choice if she gains second base due to indifference.
A.R. 220.127.116.11 In the bottom of the seventh inning with no one out, base runners on first and third bases, the base runner from first base advances to second base with no play by the catcher to prevent the winning run from scoring. RULING—Credit the base runner with a fielder’s choice to gain second base due to indifference. (See Rule 18.104.22.168 and 14.15)
The NFHS rulebook - sorry only 2010 was easy to find - also would consider this possibility, though they cover it in an oblique way. Under Stolen Base, they have only:
SECTION 55 STOLEN BASE
A stolen base is the advance of a runner to the next base without the aid of a base hit, a putout, a fielding error, a passed ball or a wild pitch. A double or triple steal involves two or three runners, respectively.
However, they do define a fielder's choice to include the traditional Defensive Indifference, as in the NCAA (and MLB) rules:
c. because of a fielder’s choice when a fielder attempts to put out another runner but is unsuccessful and the scorekeeper believes the batter-runner would have reached first base even with perfect fielding. NOTE: Scorekeepers use the term in the following ways: (1 ) to indicate the advance of the batter-runner who takes one or more bases when the fielder who handles the batted ball plays on a preceding runner; (2) to indicate the advance of a runner, other than by stolen base (F.P.) or error, while a fielder is trying to putout another runner; and (3) to indicate the advance of a runner due to the defensive team’s refusal to play on the runner (F.P., an undefended steal).
The ASA rules (link from Mastermind Ed's answer) do not include an explanation of "fielder's choice", but they do include that as part of the exceptions to what is considered a stolen base. I don't see as clear of evidence, thus, but a reasonable reading would include defensive indifference as a fielder's choice (literally) and thus, also, would mean that it would not be considered a stolen base, if it met the other criteria.