A few suggestions

1. BioGPS Easiest method is to download the datasets for your organism of choice and apply custom fold change thresholds
2. Mouse Atlas
3. Expression Atlas
4. Ensembl BioMart Under "Attributes" some species (e.g. human) have 'Expression' which can be used as a filter .

A few years back from now, I also needed this data and ended up using Tissue-specific Gene Expression and Regulation (a.k.a. TIGER). If you browse to their downloads page you will their tissue-specific genes identified either by their UniGene or RefSeq IDs.

The resource is somewhat out-dated now, but could help you get started. For a newer database, you can also try Expression Atlas that is more up-to-date, but I do not have any experience working with this data.

You could look at e g:

TiGER Tissue Specific Gene Expression database

VeryGene

You can use UniGene to query ESTs from different tissues

You can query the Gene Expression Baseline Atlas for tissue specific genes based on Illumina BodyMap 2.0; my link is an example query for liver

BioGPS can be useful

SpeCond supplementary material contains info on tissue specific genes in human

... or you could hack something on your own based on Human Protein Atlas RNA-Seq data

There are other ways too...

TissueInfo is also a nice resource: http://icb.med.cornell.edu/crt/tissueinfo/webservice.xml It provides list of tissues in which the gene is expressed and the the one in which it is predominantly expressed.

I am putting together a tool to visualize this kind of data here at the StamLab Tissue Expression Atlas, which uses RNA-seq data for fetal and adult human tissue types. It's in "beta" but we're adding more data over time; feel free to shoot me any feedback.

Genevestigator, an online application, contains a tool to identify genes specifically expressed in selected tissues. The main advantage over other tools described above is that the results are not pre-processed. You can run the search on-the-fly from the original data and combine tissues that seem to deliver similar results. It is very easy to use and is the "Anatomy" tool in the GENE SEARCH toolset. For human, you can screen across over 350 different tissue and cell types.

https://www.genevestigator.com/gv/index.jsp