There is no hard rule for verbs like the ones you mention. Spanish speakers have this tendency to turn some verbs into reflexive verbs without really needing to. Unfortunately, you'll have to ask for specific verbs when you're in doubt.
Example:
"She's combing her hair." you could say it like this:
"Ella está peinando su cabello." and that would be perfectly fine, but, in Spanish, for some reason, we got accustomed to using "to comb" as a reflexive verb more frequently, so it's more common to hear Spanish speakers say:
"Ella se está peinando." (and you can leave "su cabello" out of the sentence because it's understood)
So you can use "peinar" and "peinarse" interchangeably, the meaning doesn't change. As I said at the beginning, unfortunately, there is no hard rule. Some people have mentioned that sometimes you do this to emphasize to whom you're doing the action, but I find that explanation -with all due respect to someone that holds it- a little flaky, because sometimes it's really not necessary to turn a verb into a reflexive verb, but we still do it.
So, the verbs you ask about, like "venir" and "venirse", it's the same thing. For example, a kid might say to her friend:
"Come with me to the store!" and you could simply translate it to:
"Ven conmigo a la tienda!" but, again, Spanish speakers frequently say this:
"Venite conmigo a la tienda!" especially in several Latin American countries. The explanation? I honestly can't find one, its just a way of speaking. That happens with languages, they are not math, ha ha ha.
And to finish, the same happens with the verbs "resbalar" or "resbalarse". The last example would be:
"He slipped when walking on ice." that you can translate to:
"El resbaló al caminar sobre hielo." but you can also say
"El se resbaló al caminar sobre hielo."
Espero haberte ayudado. Buena suerte!