These resources might help if you're trying to figure out the probability of any given interspecific cross working:
https://taux.evolseq.net/CCDB_web -- Plants with the same chromosome count are more likely to successfully cross/produce fertile offspring. This site also lists some of the known interspecific hybrids within genii (look for the [genus] x [name] format).
https://www.onezoom.org/ -- You can use this to eyeball how closely related two particular species/genii are. There's surprising stuff to discover; for example, according to this chart, loquats are much more closely related to pears than apples are. The more closely related, the more likely a cross works.
For assessing the existing data on crosses, going on Google scholar and trying "[genus] hybrid" and "[genus] interspecific cross" will often turn up info.
The families are a little broad to address here, but there are some notable hybrids in most of the genera you asked about:
Solanum - lycopersicum, cheesmaniae, pennelli, habrochaites, pimpinellifolium, etc have complicated reproductive compatibility with one another
Brassica -
https://en.wikipedia.org/wiki/Triangle_of_U
Allium -
https://www.row7seeds.com/products/sweet-garleek claims to be a garlic-leek hybrid
Cucurbita - tetsukabuto is a well-known moschata x maxima hybrid with partial sterility
Cucumis - hybridization with wild relatives has been used to introduce disease resistance
Arachis - hybridization with wild relatives has been used to introduce disease resistance
Lactuca - cultivated lettuce occasionally crosses with its wild relatives
Mentha - peppermint is a notable (sterile) hybrid of spearmint and watermint
Salvia - white sage naturally hybridizes with black sage and cleveland sage
Ocimum - basilicum has notably been crossed with kilimandscharicum in recent years
Helianthus - annuus crosses with argophyllus
Rubus - basically every notable plant in this genus is a hybrid
Vicia - favas have been artificially crossed with some vetches in experimental settings
Phaseolus - some hybridization between coccineus and vulgaris
Vigna - some compatibility between radiata, mungo, umbellata and angularis
Claytonia - apparently, claytonia has significant variation in chromosome count among its species, which makes hybridization difficult
Origanum - O. x majoricum
Chenopodium - quinoa crosses with its wild relatives
The vast majority of viable interspecific hybrids have not yet been recorded.