I will try to answer this question with a combination of published evidence, personal experience, and speculation.
A) Published evidence.
The only paper I know that help answer the question is Delgado et al 2014 - Do we Need Hundreds of Classifiers to Solve Real World Classification Problems? - JMLR which runs hundreds of different algorithms and implementations on 121 datasets fro UCI. They find that although RBF SVM are not the "best" algorithm (it is random forests if I remember correctly), it is among the top 3 (or 5).
If you consider that their selection of datasets is a "good sample" of real world problems, than SVM are definitively an algorithm that should be tried on new problems but one should try random forest first!
The limits on generalizing that result are that the datasets are almost all tall and skinny (n>>p), not very sparse - which I speculate should be more of a problem for RF, and not very big (both n and p).
Finally, still on the published evidence, I recommend two sites that compare different implementations of random forests:
B) Personal experience.
I believe that papers such as Delgado et all very important for the machine learning community, so I tried to replicate their results under some different conditions. I ran some 15 different algorithms on 100+ binary datasets (from Delgado's set of datasets). I also think I was more careful on the selection of hyperparameters then they were.
My results is that the SVM was the "best algorithm" (mean rank 4.9). My take is that SVM passed RF because the original dataset contained many multiclass problems - which I will discuss in the speculation part - should be a problem for SVM.
But RF is way way faster, and it was the 2nd best algorithm (mean rank 5.6) followed by gbm (5.8), nnets (7.2), and so on). I did not try standard logistic regression in these problems, but I tried an elastic net (L1 and L2 regularized LR) but it did not perform well (mean rank 8.3)~
I have not yet finished analyzing the results or writing the paper so I cannot even point to a technical report with the results. Hopefully, in some weeks I can re-edit this answer and point to a technical report with the results.
The paper is available at http://arxiv.org/abs/1606.00930 It turns out that after the full analysis RF and SVM are almost equivalent in terms of expected error rate and SVM is fastest (to my surprise!!). I am no longer that emphatic in recommending RF (on speed grounds).
So my personal experience is that although SVM may get you some extra bit of accuracy, it is almost always a better choice to use a RF.
Also for larger problems, it may be impossible to use a batch SVM solver (I have never used a online SVM solver such as LASVM or others).
Finally I only used logistic regression in one situation. I was doing some "intense" feature engineering on a image classification problem (such as - combine or not two different descriptions of the image, and the dimensionality of the descriptions). And I used logistic regression to select among the many alternatives (because there is no hyperparameter search in LR). Once we settle in the best features (according to LR) we used a RF (selecting for the best hyperparameters) to get the final classifier.
I have never seriously worked on multiclass problems, but my feeling is that SVM are not so good on them. The problem is not the issue between one-vs-one or one-vs-all solutions, but that all implementations that I know, will use the same hyperparameters for all (OVO or OVA) classifiers. Selecting the correct hyperparameters for SVM is so costly that none of the of-the-shelf implementations I know will do a search for each classifiers. I speculate that this is a problem for SVM (but not a problem for RF!!).
Then again, for multiclass problems I would go straight to RF.