Small neutral, anionic, and cationic silver cluster hydrides AgnH and anionic HAgnH (n = 1-7) have been studied using the PW91PW91 density functional method. It was found that the most stable structure of the AgnH complex (neutral or charged) does not always come from that of the lowest energy bare silver cluster plus an attached H atom. Among various possible adsorption sites, the bridge site is energetically preferred for the cationic and most cases of neutral Ag-n. For anionic Ag-n, the top site is preferred for smaller Agn within n <= 4 while the bridge site is preferred for bigger clusters. After binding of the second H atom, the obtained lowest energy structures HAgnH- are those with two H atoms shared with only one Ag atom in anionic clusters. Natural bond orbital analysis shows that, irrespective of the charge state, electrons always transfer from silver atoms to adsorbate. Significant odd-even alternation patterns that hydrogen atoms bind more strongly with odd-electron bare clusters than with even-electron bare clusters can be observed.