In the original question, were you thinking about English or German?
The English examples you chose, e.g. and i.e., are never written out in full under any circumstances. You will not see the words exempli gratia or id est, except in a Latin class or a crossword puzzle. However, if you find yourself using the abbreviations too frequently, you may need to use phrases like 'for example' and 'that is' instead. Other Latin abbreviations include etc., cf., and n.b..
There are other German abbreviations that simply do not have any English equivalent, like bzw.. Sometimes and/or is close enough, but note that those words are so short that they are never shortened. English does, however, often use a plus-sign-like symbol for 'and' in handwriting, or the ampersand (&) in typing, and the slash (/) for 'or.'
The words 'with' and 'without' are often abbreviated to w/ and w/o. As an individual, you could choose your own short form for other words, like bc. or bec. for 'because,' or < and > for 'less than' and 'more than.'
Abbreviations are frequently used in addresses and letter writing: St., Ave., Apt., Ste., rm., tel., ext., attn:, c/o, cc:, Re: ...
Many titles are always abbreviated before names: Mr., Mrs., Ms., Dr., Prof., Gen., Sen., Rep. Some have no shorter forms: Judge, Justice.
Most units of measurement are abbreviated in daily use. Non-metric units usually have a period, at least in AE.
Certain phrases are often abbreviated in contexts like grocery lists (o.j., t.p.) or food orders (b.l.t., p.b.j.).
I'm not sure if any of that was what you wanted to know, but in case it helps.