From the Comprehensive Rules:
http://www.wizards.com/magic/comprules/MagicCompRules070201.txt408. Timing of Spells and Abilities
408.1. Timing, Priority, and the Stack
408.1a Spells and activated abilities can be played only at certain times and follow a set of rules for doing so.
408.1b Spells and activated abilities are played by players (if they choose) using a system of priority, while other types of abilities and effects are automatically generated by the game rules. Each time a player would get priority, all applicable state-based effects resolve first as a single event (see rule 420, "State-Based Effects"). Then, if any new state-based effects have been generated, they resolve as a single event. This process repeats until no more applicable state-based effects are generated. Then triggered abilities are added to the stack (see rule 410, "Handling Triggered Abilities"). These steps repeat in order until no further state-based effects or triggered abilities are generated. Then the player who would have received priority does so and may play a spell or ability, take a special action (such as playing a land), or pass, as governed by the rules for that phase or step.
408.1c The active player gets priority at the beginning of most phases and steps, after any game actions are dealt with and abilities that trigger at the beginning of that phase or step go on the stack. No player gets priority during the untap step and players usually don't get priority during the cleanup step (see rule 314.3). The player with priority may play a spell or ability, take a special action, or pass. If he or she plays a spell or ability, or takes a special action, the player again receives priority; otherwise, the next player in turn order receives priority. If all players pass in succession (that is, if all players pass without taking any actions in between passing), the top object on the stack resolves, then the active player receives priority. If the stack is empty when all players pass in succession, the phase or step ends and the next one begins.
408.1d A player may play an instant spell or an activated ability any time he or she has priority. Spells other than instants may be played during a player's main phase, when that player has priority and the stack is empty.
408.1e When a spell is played, it goes on top of the stack. When an activated ability is played, it goes on top of the stack.
408.1f Triggered abilities can trigger at any time, including during the playing or resolution of a spell or another ability. However, nothing actually happens at the time the abilities trigger. Each time a player would receive priority, each ability that has triggered is put on the stack (if it hasn't already been put on the stack). Then the player gets priority and may play spells or abilities. (See rule 410, "Handling Triggered Abilities.")
408.1g Combat damage goes on the stack once it's been assigned. For more information, see rule 310, "Combat Damage Step."
408.1h Static abilities aren't played-they continuously affect the game. Priority doesn't apply to them. (See rule 405, "Static Abilities," rule 418, "Continuous Effects," and rule 419, "Replacement and Prevention Effects.")
408.1i Special actions don't use the stack. The special actions are playing a land (see rule 408.2d), turning a face-down creature face up (see rule 408.2h), ending continuous effects or stopping delayed triggered abilities (see rule 408.2i), ignoring continuous effects (see rule 408.2j), and removing a card with suspend in your hand from the game (see rule 408.2k).
(bolding mine)
In short, yes, you get first responses to your own actions. You can add as many items to the stack as you'd like and your opponent cannot add anything to the stack until you pass priority to him. Only when priority is passed twice in succession does anything actually resolve, however.
