Omission of Subject Pronouns in Spanish
Is it informal to leave out the subject pronoun in Spanish?
Yo tengo un perro. Tengo un perro.
Of course, the conjugation gives away what the pronoun is, but is it informal, like in English?
Example in everyday speech:
Questioner: What did you do today? Respondent: I went running. OR Respondent: Went running.
The second response, here, is very informal.
No, it is not informal. Subject pronoun is not needed most times because verbs have endings that mark the subject. Then, the default option is not using the pronoun. People who uses pronouns a lot can sound childish, foreign* or arrogant (We have a saying: "You resemble a yo-yo: yo yo yo.")
"Tengo un perro" is clear about the owner. You can add "Yo" in order to focus or emphasize something, like in "A: Tengo un gato. B: Yo tengo un perro". Observe that A is using the default option and B needs to focus on him/herself. When a conjugated form is the same for different subjects, it can be used the pronoun for clarity: "[Usted] canta bien" (statement) vs "[él/ella] canta bien" (statement) vs "canta bien [tú]" (command).
*Apparently right texts in Spanish written by English speakers or translated from English usually have more subject pronouns than normal. It is a clue of "foreignness".
Both of them can be informal or formal. It doesn't matter. But when you want to say something crearly it's better if you say the number of items that you have. For example:
"Tengo varios bolígrafos, puedo prestarte uno" ---- "Tengo tres bolígrafos, puedo prestarte uno"
If you say the number too, it will be clear but it's not like you will need to say it ALL the time.