Data on health status of patients can be high-dimensional (100+ measured/recorded parameters from blood analysis, immune system status, genetic background, nutrition, alcohol- tobacco- drug-consuption, operations, treatments, diagnosed diseases, ...)

Multiple measurements from each sample. Suppose that a gene expression experiment was conducted using microarray in two groups (case and control) with 4 replicates of each. Each sample would have gene expression values for thousands of genes which is “high dimensional” data set.

Most of ecological data are high dimensional. For instance, suppose we have 200 plots and 150 species totally for a sociology analysis. Plots are repetitions and species are dimensions.

Data on health status of patients can be high-dimensional (100+ measured/recorded parameters from blood analysis, immune system status, genetic background, nutrition, alcohol- tobacco- drug-consuption, operations, treatments, diagnosed diseases, ...)

High dimensional data are data characterized by few dozen to many thousands of dimensions (see the definition of high dimensional data in the CHDD 2012 international conference https://sites.google.com/site/chdd12naples/). You can some examples here:

Example of High Dimensional Data (Allen 2011).

http://www.stat.rice.edu/~gallen/examples_high_dim_data.pdf

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any data set representable under a relational model (fact tables linked in 0:N to the central table) is intrinsically infinitely dimensional (loosely speaking) : the flattening of such a representation (that is building a flat table with one individual per line and one constructed feature per column) will produce as many constructed features (columns) as your imagination can think of and the set of informatic programs (or the subset of primitives and combination rules you have restricted your flattening to) will allow !

so, in principle, any data set as structurally "simple" as a web log (or any interaction log : purchase, phone calls, ...) indeed spans a very very high -dimensional space

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Repeated time or space related measurements in any field of study tends to be multivariate in nature. Hence, examples from many different fields can easily be collected.

Analysis of shapes of contours is one example of data analysis in infinite dimensions. That is data analysis on the projective spaces of a Hilbert space, which is a Hilbert manifold Of course in practice that is done using high dimensional approximations. .

Financial data is somewhat high dimensional. For instance, you can observe prices on stocks daily, hourly, minutely, secondly, ... In the US, perhaps 2000 - 3000 stocks are readily monitorable. Additionally, there are thousands of traded portfolios, ETFs, that are linear combinations of the underlying stock prices. And, there are stocks from other countries that trade during US hours, ADRs.

I find financial data interesting because relationships change overtime (General Electric is a manufacturing company that became a financing company among other characteristics). The number of observables changes over time too. Companies are born (IPOs or spinoffs), live, and then die (bankruptcy or takeover). I think other domains have "sensors" with finite life spans, so its interesting to me to think of company prices as sensors for an economy or industry with finite life spans :)

You could also drill down to another, smaller scale, and obtain order data ("buy 100 xyz at $50", "sell 200 abc at $37") at millisecond or finer resolution. The "book" (collection of all live orders in a stock, typically some to buy, and some to sell at various prices) dynamics are interesting to model.

Outside my field, I always thought weather forecasting / sensing was an interesting high dimensional domain.

Not sure if it's too late to answer, but many applications in computer vision deal with high-dimensional data. One example is the following basic facial recognition algorithm. Suppose you have n images, each with a resolution of m pixels by k pixels. We can view each pixel within the image as a variable, so that each of the n images resides in an m x k dimensional space. From there a training set of images is used to recognize new faces. Depending on the application and the images, we may be able to represent the training/new images with a lower dimensional sub-space.  

http://en.wikipedia.org/wiki/Eigenface

Earth Observation Data/ Geographical data is a classical example of High Dimensional Data. Same is also a classical example of spatio-temporal data too. In this scenario data may have 100+ dimensions e.g. longitude, latitude, temperature, pressure, rainfall, humidity, altitude, time, season , soil type,  and  many more( if data is in vector format). If data is in raster format i.e. image which can always be considered as multidimensional data, as answered earlier by Measy  G.

We can help you in much better way, if little bit more details about your work are  known to us.

High dimensional data can be obtained from different sources, depending on what kind of process one is interested in. Any process in nature progresses as a result of many different variables, some of which are observable or measurable and some are not. Hence, multivariate data can be obtained from any field of study, though the degree of difficulty in the collection of such data is highly variable. In view of this general remark, one can appreciate the work involved in acquiring high dimensional data.

As we know that in any study, the information regarding variables which need to interact are arranged in various rows and columns in a matrix. If the size of  matrix keeps on increasing vastly as more than five cross five or ten cross ten, it gets difficult to discern and categorized as high dimensional or big data or mega data etc. High dimensional data is high, will be judged and calibrated by concerned domain expert not by any other expert.  It will vary from system to system.

High dimension is when variable numbers p is higher than the sample sizes n i.e. p>n, cases.

For example, tomographic imaging data, ECG data, and MEG data.

One example of high dimensional data is microarray gene expression data.

High dimensional data is referred to a data of n samples with p features, where p is larger than n.

Dimensionality of a laser reading/laser spectrum is 25,000+. Now a days, laser based classification gaining its importance in the field of material classification, remote sensing, and historical identification problem etc.

Ex. LIBS Data