Via some trial and error, read experimentation, I have been able to find a couple of reasonably accessible websites for viewing Telenovelas. Three of them have some form of English close captioning available, while the forth does not appear to have anything of the sort.
The first, is
Hulu Latino edition! I've enjoyed using hulu's services in the past, and the only negative I can think of is that they don't keep a large catalog of old episodes, but then again, that's what netflix is for. From a viewing standpoint, Hulu Latino is a mixed bag. It does have a decent selection, but the prevention from viewing the shows original episodes must be considered. Another large thing to consider is that the close captioning leaves something to be desired. Of the few Telenovelas I tried here I had about a 50% success rate when it came to the show actually having English close captions. This isn't necessarily a negative thing, but if you're of little to no education in the Spanish language, or don't want to be constantly pressured to translate as you watch, then this might take a little digging to find what to watch.
viki.com has, at the time of this articles creating, 48 series that they have labeled as Telenovelas. The selection has some diversity when it comes to country of origin (some coming from places like Turkey, Pakistan, and Thailand), but I can comfortably say that around a third of the titles are arriving out of Venezuela. I will say that the majority of the titles have near complete English captioning, but there is an easy to access label displayed before selecting each series that shows how much has been properly captioned. Both easy to find what is monolingual-ly accessible, and an opportunity to help the websites community by translating and helping create the needed captions, the site is interesting, a certainly one to look at. It is also worth note that the site features a large collection of Korean Drama series that are also English captioned.
DramaFever is similar in several respects to the above mentioned viki.com, but I find that the accessibility to be much higher. The site features several sorting options like ordering based on popularity, release date, or rating. It is also easily apparent from the main list several pieces of information that will assist in quickly picking a series. These would be a brief summary of the title, the community rating (in the ever common five stars system), the base language, and the captioning language (English in the cases I've seen).
The final site I'm putting here is
Ver Mi Telenovela. Ver Mi Telenovela is different than the other three here, in that it, to my knowledge, doesn't feature any sort of translation closed captions. It does seem to feature a nice collection of pieces, and seems like it would be good if one didn't need assistance in their viewing. This could also be useful is you wanted to watch as a test of knowledge without the crutch that captions provide.
There are many different sites to view Telenovelas and their equivalent forms of media, these are just to give you a head start.