There are two phenomena in play in your examples. They are sometimes indistinguishable from each other:

• Was re-installing a workstation in a conference room;
• Discussed a quarterly report with X;
• Am on an expo in Chicago;

The first phenomenon is that of very informal speak, omitting the word subject I (and sometimes even the verb, as in my last two examples):

• Am on an expo in chicago.
• How are you? Am fine.
• Where are you going? On the way to the store.
• In a hurry, can't talk now.

Etc.

The other is the use of passive voice. This may be used in formal writing, or when describing something in general, without a specific subject in mind. The implied subject can be "we", "they," "I", "the boss," "the team," or anything else that fits the context. These sorts of things might be seen on an itinerary (in present or future tense), the minutes of a meeting or an executive summary (in past tense):

• (I|he|we|they) Discussed a quarterly report with X
• [Possibly] (I|he|the intern) Was re-installing a workstation in a conference room;
• (I will|we will|they will) Attend banquet.
• (I will|the students will) Receive awards.
• (I|the committee|the boss) Assigned tasks.

It is very casual and informal. When in doubt, I recommend that you do not use it. It is quite different from Italian or Spanish, where subject pronouns can be left out; in English (and other Germanic languages), it is unusual. I would interpret it as follows:

1. You are in a hurry or working on an awkward keyboard;

2. Or this text is not important;

3. Or you are consciously mimicking a casual, conversational style.

Because journals (not academic journals, but logbooks) and diaries are to be considered one's own notes and regularly written in a hurry, people may leave out subject pronouns more often in those genres. For that reason, omitting subject pronouns has come to evoke a journalling style.

In many genres of texts, it is considered bad style, unless it is part of a dialogue that is meant to sound colloquial. So I wouldn't use it in a novel, a newspaper article, an academic paper, an e-mail to a stranger, nor in most other genres.

This crops up rather frequently because some people will compose a letter similar to the way we might give an answer over the phone, particularly when we are in a hurry. While I'm proofreading my email, I'll often notice I've done this – but it was generally inadvertent, and I usually change it, and add the subject, after I've noticed I've done it.

As Cerberus said, the language is informal. Works fine in conversation but can read awkwardly on the other end.

Incidentally, this doesn't only occur with "I"; it can happen when the subject is "it" as well (as I showed in the last sentence of my previous paragraph – although, in that instance, I did that intentionally to illustrate a point).

Others have answered the part about omitting "I". Let me just add that people writing informally often omit pronouns and articles, and sometimes prepositions. Like, in formal writing we might say, "Bob came yesterday. He helped me to set up the computer. After that we worked on our presentation." In informal writing one could say, "Bob came yesterday. Helped set up computer. After that worked on presentation." For the most part the reader can guess what the correct pronouns, etc are, though you might note that there is some ambiguity. Did Bob help me to set up my computer, or did I help him set up his? Etc.

RE beginning too many sentences with "I": In general, we try to avoid using the same word or sentence pattern repeatedly because it tends to sound odd. If I started to write, "I drove my car to a car dealer where the car salesman sold me a new car", I would probably rework that, maybe to, "I drove to the auto dealer where the car salesman sold me a new vehicle." With the word "I", there can be the additional implication that, depending on the context, it can make you sound self-centered, like everything in the world is about you. For example, in business circles it is very common advice to talk about what "the team" did rather than what "I did".

If you are writing some sort of narrative and you find yourself writing, "I did X. Then I did Y. Then I did Z.", this tends to sound very repetitive and boring. You should try recasting it, like "I did X. After that, Y had to be done. Z was also important." (Of course what alternative wording works depends on just what X, Y, and Z are in context.)