I like the video clarity and quality of the Nikon D3100. However, it has a time limit on it, which I don't like.
How can I go about finding an HD camcorder with similar video clarity to this camera, but without such a limit?
I am not certain I understand why you need to shoot a scene for longer than 10 minutes. Most of the movies I make are under 4 minutes and include up to 30 or more shots some lasting less than a 1/4 second while others may last a minute. I only mention this to give you an idea what I am used to. I have both a camcorder that can shoot as long as there is memory--up to an hour possibly, and I have a pocket point and shoot that has time constraints based on format, not unlike the Nikon D3100.
Assuming you have a need to shoot a scene for longer than 10 minutes such as a traffic study or to document a school play I will proceed to address the issues.
Reviewing the tech specs of the Nikon D3100 I see the following HD movie settings:
HD 1,920×1,080 / 24 fps
HD 1,280×720 / 30 fps
HD 1,280×720 / 24 fps
Noting that these all have a 10 minute recording limit.
Many DSLR cameras are bound to a 10 minute recording limit due to the way the firmware/software is designed to handle memory storage. Many cinematographers and photographers alike are pushing to have this issue addressed as in allowing for longer takes so you are not alone.
Choosing a camcorder is a reasonable alternative but there will be tradeoffs. Here are few that come to mind. YMMV (your mileage may very).
1) The "Glass": the Nikon D3100 has a removable lens so you can swap in other lenses of different focal lengths and quality while most camcorders have a non-removable zoom lens.
2) FOCUS: the Nikon D3100 will allow you to change focus while shooting video while most camcorders do not allow you to manual focus on the fly or make this difficult by not having a focus ring on the lens but an external wheel which generally causes camera shake.
3) Shutter Speed: I am uncertain if the Nikon D3100 allows for changing the shutter speed while shooting video, but more advanced DSLRs will, e.g. Canon 5D Mark II. This is a significant feature for cinematographers engaged in time-lapse movies, where 'drag the shutter' is very desirable.
(NOTE: one thing you will trade up to is that the Nikon D3100 only records in mono, while almost every camcorder records in stereo if not Dolby 5.1 Surround.)
Here is a criteria that might assist you in choosing a camcorder. Since the price of D3100 is nearly $649 USD MSRP, then you might consider using this as a baseline for your search in that price range e.g. Sony HDR-CX260V/T about $549.
Alternately you might consider the clarity and quality of the lens on the Nikon D3100 so choosing a Panasonic TM900K that comes with a Leica 12x zoom should be a pretty good contender--about $900.
Or perhaps you favor a camcorder that allows you to use a variety of lenses such as the Sony NEX-VG10 or NEX-VG20H--nearly $2000.
You might want to review the specs of each of these camcorders and visit local stores to give them a test ride.
One very important point, be sure that the camcorder you choose has a video format that works well with your current video editing software, this can definitely be a show stopper. Currently your Nikon D3100 uses .mov files while Sony uses AVCHD and Panasonic has their version of AVCHD. You might want to join .mov files to work with another format so you want to be sure that they all get along in the same video suite.