Since you’re asking about reduplicated perfect (and not reduplicated present, as in bibo < *pi-ph3-e or sero < si-sh1-e, Weiss 2009: 405), I will try to address perfect formation only.
One of the problems is that synchronically we may not see all cases of reduplicated perfect in Classical Latin. However, by drawing on data from Old Latin and other Indo-European languages (especially from Greek, Sanskrit or Anatolian languages), we may discover more interesting cases.
For instance, Baldi mentions that
“Vowel weakening and the accompanying syncope have caused many Latin verbs with inherited PIE reduplication to lose the vowel of the reduplicated syllable” (p. 378).
Tronskii 1960 (2003) argues that if a reduplicated form had more than three syllables, the extra syllable was syncopated (para 624):
- compound verbs: rettuli (*retetuli), reppuli (*repepuli), reccidi
(*rececidi), repperi (*repeperi) etc.
- cecidi but: occidi (*ob-cecidi), concidi (*con-cecidi);
- tetigi but: contigi;
- spopondi but: respondi;
- tetuli but: abstuli (*abs-tetuli), attuli, sustuli etc.;
- dedi or condidi but: abscondi;
- converti (*conveverti);
- incidi (*in-cecaidi) etc.
Tronski also mentions that tetuli was ousted by tuli, scicidi by scidi, tetendi by tendi etc. He also talks about some verbs that changed their perfect formation type because of syncope, e.g. tetini and continui etc.
Baldi also discusses Mester 1994, who examined the distribution of the three most common perfect formations. Baldi sums up by saying that perfect formation can be determined by prosodic, analogical, morphological and frequency factors.
Weiss 2009 writes that "verbs of second conjugation have u-perfect if the stem is light, but some other formation (s-perfect, reduplicated perfects) if the stem is heavy" (p. 413).
doceo - docui
BUT:
augeo - auxi
mordeo - momordi
He mentions a number of exceptions to this rule, though.
Now, if you really need a list of most common verbs that have reduplicated perfect, here's one, from Borovskii and Boldyrev 1975 - by no means exhaustive.
First conjugation:
do – dedi
sto – steti
- praesto – praestiti
- obsto – obstiti
Second conjugation:
mordeo – momordi
pendeo – pependi
spondeo – spopondi
tondeo – totondi
Third conjugation:
cado – cecidi
caedo – cecidi
pendo – pependi
tendo – tetendi
- attendo – attendi
- ostendo – ostendi
credo – credidi
vendo – vendidi
perdo – perdidi
addo – addidi
- condo – condidi
- abscondo – abscondi
parco – peperci (parsi)
fallo – fefelli
cano – cecini
curro – cucurri (cf. Old Latin cecurri)
- accurro – accurri (accucurri)
posco – poposci
tundo – tutudi
tango – tetigi
pango – pepigi (pegi, panxi)
pungo – pupugi
pello – pepuli
disco – didici
sisto1 – (stiti)
sisto2 – steti
- circumsisto – circumsteti
- obsisto – obstiti
- subsisto
- desisto
- resisto
- existo
Third conjugation (io):
pario – peperi
Fourth conjugation:
comperio – comperi
reperio - repperi