If altruism is defined as:
"To act without conscious expectation of reward", then it is quite easy to imagine situations in which a person might act 'purely' for the benefit of another.
Instantaneous reactions - such as the trope of throwing oneself on a grenade - might occur prior to any consciously-recognised evaluative processes during which the reward of 'doing one's duty' or 'being a hero' is taken into account.
It is another thing however to argue that such an act is therefore not motivated by some kind of reward. It is quite possible that motivations such as to 'be a good soldier' for example, drive instinctive acts such as these at such a speed that the conscious mind - occupied with the urgency of getting to the grenade in time, and possibly with fear - is simply unable to register.
Even if an act is 'automatic', there is almost always going to be a motivator that leads the mind to pursue one particular automatic response instead of another (such as to flee from the grenade). In the absence of such motivators, there would be no reason for the soldier to move towards the grenade.
In the case of the soldier, such a motivation likely has roots in the heavily team-oriented values embedded during training, and in any personal values which led to the soldier becoming a soldier in the first place. A desire to prove one's masculinity to oneself or others. Patriotic values. Family tradition. There are many other potential motivators of course, such as love, perhaps, for a particular colleague in harm's way, or even a suicidal impulse that seeks to avoid the suffering that would be sustained by a non-lethal but traumatic injury. Another powerful motivator might be to avoid the shame/dishonour/guilt/remorse of not sacrificing oneself when one had the opportunity to do so.
All of these motivators, regardless of whether or not they serve partially to help the other, seem to always have an origin in, and a desire to serve, the self. Even the self-sacrificial act satisfies some value that the self holds as important. In the case of the soldier described above, many of these motivating values boil down to the importance of being a 'good person', not only in the eyes of others, but in his or her own eyes.
Less urgent actions have been addressed clearly in earlier answers. Suffice to say, acts we might consider more fully, more consciously, such as the donating of money, or the giving of time, or the uttering of a charitable word, will always provide the giver with reward, whether it be an affirmation of values, the immediate feedback of a person's gratitude, or again, the avoidance of any negative emotions that might arise from acting against one's values.
So, whilst it easy to imagine the 'unthinking', 'noble' act as altruistic, it is far more difficult to conceive of an unmotivated act. An unmotivated act is necessary for the 'true' altruism of which you enquire, for when we act in accordance with out motivations, we cannot help but be rewarded.
If you can imagine an example of an act which does not provide some form of reward to the actor, I would sincerely enjoy reading about it.