There are lots of pre-existing case (everyday use) of verbs with re- before: rebondir, rejaillir, retordre, retrousser…
But the re- form enables you to make new verbs with a meaning of repetition or not, which are not provided (directly) by the French language. You can use the re- before a verb with almost every verbs or nouns in French.
A very good article form the Office Québécois de la langue française: le préfixe re-.
Or some examples in the french Wikitionary.
First, the re- prefix doesn’t always connote re-petition (e.g. recompter), it may also indicate re-currence (e.g. rebondir), re-action (e.g. rebondir with a different meaning), re-adjustment (e.g. rehausser), or state re-covery (e.g. revenir), re-ciprocity (e.g. redevoir), among others.
Quite a few verbs do not admit such a prefix. I would advise you against making words you have never seen. Prefer adverbial locutions such as “de nouveau”, “à nouveau”, “une fois de plus”, “encore une fois” to express repetition.
Note: resavoir does not exist, it sounds very odd and would not be understood (with whatever meaning); reconnaitre exists but its meaning is very different from connaitre.
You can do it in most cases and it should be understood: reparler, remonter, revoir, reprendre, recourir, relire…
but it will sound weird in some cases, even if it makes sense: raimer (aimer), se révanouir, rehaïr, repréférer, recomprendre…
and in some cases it means something else entirely: réviser, reporter, remiser, répondre, ressentir, regarder… and in this case, adding another re- will sound awkward.
So I would advise to do it in informal context, and especially orally: native speakers do it all the time, I have even heard « J’ai re-ressenti » and « J’ai re-regardé » ; but you shouldn’t try it in formal context, or in write it if you are not sure of how it sounds. Note that it should be ré- before a silent h as in réhabituer and in some cases before a vowel réarmer, réapprendre.
For more insight on using re-, le wiktionnaire has good usages notes.
Now if you are not sure or don’t want to use re-, in most cases, and especially for dynamic verbs, using encore is a good replacement in composite tenses
J’ai rejoué → J’ai encore joué
while de nouveau sounds right in simple tenses
Je rejoue → Je joue de nouveau