The highest level I've ever hit with 4e is 4th, barring a single session we played of "Tomb of Horrors" which was, of course, at much higher level (12th?).
Basically, if the game starts at 1st level, I wouldn't expect to hit Epic levels, even if the DM stated that he was wanting to run a long-term campaign, and even if he had the party level up after every session! Even at that rate, that's still 20 sessions, which is about a year of gaming with our current schedule, and fatigue has generally crept in by then.
The highest level I've ever seen achieved "fairly" with characters who started at level 1 was 18th, in the "Shackled City" Adventure Path in 3.5e. (They would have reached 19th if we'd bothered handing out XP at the end of that last session.) But by that point we were rather glad that the campaign was definitively over, and wouldn't have considered carrying on - we certainly would never play Epic in 3.5e.
My current campaign (also 3.5e) is intended to go into the high levels, probably 15th or so. But, again, there's no way it will be reaching Epic levels.
In order to reach Epic levels, I think the game needs to be very carefully planned, and there needs to be a certain determination on the part of the group to stick it out. (Also, I think a fairly high rate of level-gain is a must.) Otherwise, the attraction of the new and the shiny, coupled with fatigue, is likely to creep in after 6-8 months, and you don't get anywhere.
Which is a shame, since I do think Epic play does (or at least can) offer an experience that you don't really get with the lower levels. Sure, you can play "save the world" at 1st level, but it kinda feels like cheating, especially if all you beat to achieve this is a glorified bunch of kobolds!
So I think perhaps the way to go is actually deliberated Paragon and Epic campaigns - campaigns that deliberately start at the start of the respective tiers, run for 10 levels, and then stop. It means breaking down that odd prejudice against starting at higher than 1st level, but otherwise should be a valid approach.