Check Google Scholar here, search ArXiv for recent papers, and consult the Department of Statistics Technical Reports

Golden Oldies — Mathematics of Signal Processing — Pre-Internet Papers that still get cited:

Donoho, D.L.  (1981)  On Minimum Entropy Deconvolution.  In Applied Time Series Analysis, ed. D.F. Findlay.  New York: Academic Press,  565-608.

Donoho, D.L. and Stark, P.B. (1989) Uncertainty principles and signal recovery. SIAM Journal of Applied Math, June 1989, 49,  pp. 906-931.

Donoho, D.L., Johnstone, I.M., Stern, A.S. and Hoch, J.C. (1992) Maximum Entropy and the Nearly Black Object (with discussion). Journal of the Royal Statistical Society, Series B, (1992) 54, 1, 41-81.

Donoho, D.L. and Logan, B.F. (1992) Signal Recovery and the Large Sieve. SIAM Journal of Applied Math. April 1992, 52, 577-591.

Donoho, D.L. (1992) Superresolution via Sparsity Constraints. SIAM J. Math. Anal. Sept. 1992, 23, 1309-1331.

 

Golden Oldies — Mathematical Statistics — Pre-Internet Papers that still get cited:

Donoho, D.L., Liu, R.C. and MacGibbon, B. (1990) Minimax risk over hyperrectangles and implications. Annals of Statistics, 18, Sept., 1990, 1416-1437.

Donoho, D.L. and Nussbaum, M. (1990) Minimax Quadratic Estimation of a Quadratic Functional.  Journal of Complexity, 6, June 1990, 290-323.

Donoho, D.L. and Liu, R.C. (1991) Geometrizing rates of convergence II. Annals of Statistics, 19, June 1991, 633-667.

Donoho, D.L. and Liu, R.C. (1991) Geometrizing rates of convergence III. Annals of Statistics}, 19, June 1991, 668-701.

Donoho, D.L. and M.G. Low (1992) Renormalization Exponents and Optimal Pointwise Rates of Convergence. Annals of Statistics, June 1992, 20, 944-970.

Donoho, D.L. and Johnstone I.M. (1994) Minimax Risk over $l_p$  balls.  Probability Theory and Related Fields, September 1994, {\bf 99}, 277-303.

Donoho, D.L. (1994) Statistical Estimation and Optimal Recovery.  Annals of Statistics, 22, March 1994, pp. 238-270.

Donoho, D.L. (1994) Asymptotic Minimax Risk for sup norm loss: Solution via Optimal Recovery. Probability Theory and Related Fields, Sept. 1994, 99, 145-170.

Donoho, D.L. (1995) De-Noising via Soft-Thresholding. IEEE Trans. Info. Theory, 41, May 1995, pp. 613-627.

Donoho, D.L. and Johnstone, I.M. (1995) Adapting to unknown smoothness via wavelet shrinkageJourn. Amer. Statist. Assn. vol. 90 no. 432, December 1995, pp. 1200-1224.

Donoho, D.L., Johnstone I.M., Kerkyacharian, G., and Picard, D. (1995) Wavelet Shrinkage: Asymptopia?  Journ. Roy Stat. Soc. Ser B,  57, no. 2, 1995, pp. 301-369.

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding. Annals of Statistics 24 508-539.

Donoho, D.L., Johnstone I.M. (1996)  New Minimax Theorems, Thresholding, and Adaptation. Bernoulli,  2, 1996,  39-62.

Donoho, D.L. and Johnstone, I.M. (1998)  Minimax estimation via wavelet shrinkage. Annals of Statistics 26, 3, 879-921.

 

Barely Published, but had some impact

Donoho, D.L. and Huber, P.J. (1982) The notion of breakdown point.  In Festschrift for Erich Lehmann, K.A. Doksum and L.L. Hodges, Jr., eds.  Belmont, CA:  Wadsworth.

Donoho, A.W., Donoho, D.L. and Gasko, M. (1988) MacSpin: Dynamic Graphics on a desktop computer. IEEE Computer Graphics and Applications, June 1988, pp. 51-58.

Coifman, R.R. and D.L. Donoho (1995) Translation Invariant De-noising. Wavelets in Statistics, A. Antoniadis and G. Oppenheim Ed. pp. 125-150. New York: Springer- Verlag.

Buckheit, J.B. and D.L. Donoho (1995) WaveLab and Reproducible Research. Wavelets in Statistics, A. Antoniadis and G. Oppenheim Ed. pp 55-82. New York: Springer- Verlag

Donoho, D.L. and Yu, T.P.Y. (1999) Deslauriers-Dubuc: Ten Years After. Spline Functions and Wavelets. S. Dubuc and G. Deslauriers, eds. pp. 353-370. Providence, Amer. Math. Soc.

 

Unpublished for surprising reasons, but still close to my heart.  Probably some of this could still be properly published.

Donoho, D.L. (1998) Counting Bits with Kolmogorov and Shannon.

Donoho, D.L. (2000) High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality.

Donoho, D.L. (2002) The Kolmogorov Sampler.

Donoho, D.L. (2006) Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations.

Donoho, D.L., Johnstone, I.M. Maleki, A., and Montanari, A. (2011) Compressed Sensing over $\ell^p$ balls: minimax mean‑squared error.

Donoho, D.L. and A. Montanari (2015) Variance Breakdown of Huber (M)-estimates: $n/p \rightarrow m \in (1,\infty)$.