Depends on many factors but as a rule I'm all for it.
In "olden days" it was traditional for the wine steward in royal and noble households to taste the wine, not so much to check its quality but as a sign that it was not poisoned. Following the French revolution, during which time restaurants as we know them today began to open, it became traditional for the sommelier first to pour a tiny bit of wine for himself to taste, and only then to offer a first small tasting pour for the host at the table. That tradition has remained firm, especially in France and Italy at restaurants that employ true sommeliers. It is not traditional for wine waiters or others than the sommelier to do such a tasting.
In Europe, I'm all for the tradition in restaurants that have true sommeliers but on the conditions that the bottle will be opened at my table (I will never accept a bottle that has not been opened at my table), that the sommelier asks if we would like him to taste, and of course that he takes just enough of a quantity (20-25 cc) for his tasting. After his tasting, I expect that either I or whomever is the host will be given a small amount as a tasting sample as well. One of the advantages of this is that it can, if desired, lead to a discussion with an informed sommelier on the qualities of the wine and perhaps a comparison to other similar wines or the same wine of other vintages.
In America, from the mid-19th century and the days of better restaurants such as Delmonicos, the tradition persisted and such restaurants did have well trained sommeliers, most of whom had received their training either in France or the UK. Later, as American restaurants became more mass-market oriented, the sommelier was replaced by the "wine waiter" or even by the waiter who was supposed to (but did not necessarily) know something about wine. Only a few American restaurants kept the habit and those (e.g. The Starlight Room at the Waldorf Astoria, the Columns at the St. Regis, etc) of keeping a true sommelier …..until the late 1980's and early 1990's when restaurateurs realized once again that a good sommelier was as important a part of the staff as the chef. By then, however, it had become a matter of individual choice – at Boulud the sommelier offered to taste; at the Four Seasons, it was considered a faux pas, etc. The habit of the sommelier tasting took off in a major way with the advent of fine restaurants in (of all places) Las Vegas, and has since spread both east and west.
My own policy in the USA is to determine whether there is a real sommelier and what his background is. If it is a European equivalent, I will let him taste my wine with pleasure and then go on to my own tasting. If the sommelier is, as is too often the case, an oenological illiterate, I insist on doing my own tasting. With older bottles I will even insist in such cases on opening the wine myself. In some case, where a wine should be opened 1 – 3 hours before being served, I will appear at the restaurant either to open the wine myself or to oversee its opening.
In Israel we're faced with a different story – too many so-called sommeliers having neither adequate training or knowledge. In my own case I'm fortunate enough to know each of the sommeliers at the various restaurants and make my decision based on personal knowledge. Let's put it this way – at any restaurant that I rate 5 stars and at a few that rate 4, I'll be glad to put myself in the hands of the sommelier, sometimes in fact ordering my dinner and trusting the sommelier to actually select the wines for me. In far more cases – helas – I go entirely on my own and insist on that. The good news is that there is an increasing number of well-informed, well-trained sommeliers here in Israel.\\
To a second point – when I bring my own wines to a restaurant (probably about 50% of my visits), I will always offer the sommelier or wine waiter and perhaps the chef a small glass for their pleasure. At times, if the wait person is really nice I will even "insist" that they too try the wine. Indeed, one of the pleasures of wine is sharing. When ordering wine from the restaurant menu if the wine waiter/sommelier/wait person is not familiar with the wine I will often offer a glass for their tasting pleasure.
But then again, I'm said to be an old-fashioned person.
P.S. In European households even today it is considered traditional for the host to taste the first glass of the wine. From a pratical poiunt of view that is done to check the wine. From the traditional point of view it remains a sign that the wine he/she is about to offer guests has not been poisoned.