I know that it's not effective to train the same muscle group every day because the muscle needs time to recover.
Indeed, the key parameter here is that training the muscle essentially involves damaging it (micro-tearing the muscle fibers) and then letting your body act as the repair man; this is a process that as you noted takes time.
With streching there is no "damage"/tearing inflicted on the muscle (except possibly by over-streching a muscle) rather there is a "lengthening" of the fibers (see comments for more on this)*. To sum up, it's something you can do daily if you need to but as the following recommendations/studies show, that isn't necessary.
Is it still effective to stretch the same muscle group every day or should I make a pause of 48 hours to give the muscles time to recover?
To add another source for this, I was recently looking at Current Concepts In Muscle Streching For Exercise and Rehabilitation which, as described in the Abstract, is:
The purpose of this clinical commentary is to discuss the current concepts of muscle stretching interventions and summarize the evidence related to stretching as used in both exercise and rehabilitation.
The information presented is probably more than what is required to answer your question but it does provide a referenced answer to most things streching related. In the recommendations section we see that:
For a general fitness program, the American College of Sports Medicine recommends static stretching for most individuals that is preceded by an active warm-up, at least 2 to 3 days per week. Each stretch should be held 15-30 seconds and repeated 2 to 4 times.
The referenced recommendation is a book continuously updated every 4-6 years with contributions from many authors; I can't see any reason to doubt its validity.
Either way, this does give a frequency for streching but doesn't necessarily answer if doing it daily might have negative effects.
For that, another study, namely, Effect of Stretch Frequency and Sex on the Rate of Gain and Rate of Loss in Muscle Flexibility During a Hamstring-Stretching Program: A Randomized Single-Blind Longitudinal Study whose goal was to:
This study evaluated the effects of 4 different weekly stretching protocols on the rate of gain and decline in hamstring flexibility over an 8-week period, across sex.
Helps. The conclusion reached in this study shows:
Stretching appears to be equally effective, whether performed daily or 3 times per week, provided individuals stretch at least 2 times each day. Moreover, although women are more flexible than men are, there was no sex difference in terms of stretching response.
(Note, no mention of the "type" of streching they used)
The reason I have added the (Notes) in the preceding quotations is because the type of streching you do is important. Recent studies have indicated that performing static streches before a work-out can be detrimental whereas dynamic streches might reap benefits (and *static ones after done with the work-out).
I mention this over here because it is an important aspect of streching, there's different kinds that need to be understood and incorporated correctly. A referenced article by muscleforlife seems to break these down nicely, give it a look if you want to learn more.
*) The comments by JohnP and JaredW82 contain further information regarding the effect streching has on the muscle, for a good read, check them out.