Some websites - mainly for URL shortening - have short domain names. Now my question is: How can I register two-letter domain names like aa.com or bb.in?
By default, many authorities restrict the use of 1- or 2-letter domains for special uses (for states, organisations). The most frequent regulation appears to be a 3-letter minimum. And - to be sure - for .com and .net and the like is probably too late.
But some authorities (of a nation like West Samoa) allow these short domains. You could try all the registrars though and see what the come up with when you look for 2-letter names. You might be lucky with some obscure TLD like .pw (Palau) or .mp (Northern Mariana Islands).
And even if the domains are not in the search results, they may be for sale (for the right sum). You would have to contact the domain authority to get authorization to register a 2-letter domain name and to learn what it would cost.
Here are some sources:
If you're flush, you can participate in an auction to buy a two-letter domain (e.g. http://www.buydomains.com/find-premium-domains/search-results.jsp?length_min=2&length_max=2&category=twochar - not affiliated).
Good luck finding one!
There are quite many registries allowing 2-characters. If you choose an European ccTLD probably you will not have to pay more money for 2-char than for usual domains. In case of exotic TLDs sometimes there might be a special price for 2-chars, higher than for normal. Be also aware that there are some not serious ccTLDs out there - heard of stories where the TLD was disconnected from internet for weeks, or the prices rised very strong next year. If you are looking for business purposes maybe it makes sense to order a reseller like 1-single-letter-domains.com to find a domain for you. They offer even shorter 1-char domains, but they are quite expensive.
I threw together a perl script to hit domai.nr and see which TLDs allow 2-character domain registrations. Here is the script:
It took about 2 minutes to run through all 276 TLDs in the list. Here are the ones that allow 2-character registration:
.aero, .af, .ag, .ai, .an, .ao, .ar, .arpa, .au, .az, .ba, .bd, .be, .bf, .bh, .bj, .bm, .bn, .br, .bv, .bw, .by, .bz, .ca, .cat, .cc, .cd, .cg, .ck, .cl, .cm, .coop, .cu, .cv, .cw, .cx, .cy, .cz, .de, .dj, .dk, .dz, .edu, .ee, .eg, .er, .et, .eu, .fi, .fj, .fk, .fm, .fo, .gb, .gd, .gg, .gh, .gl, .gm, .gn, .gov, .gp, .gq, .gs, .gu, .gw, .gy, .hk, .hn, .ht, .hu, .id, .il, .int, .io, .iq, .ir, .je, .jm, .jo, .jobs, .jp, .ke, .kg, .kh, .km, .kp, .kw, .kz, .lb, .lc, .lk, .lr, .ls, .md, .mf, .mh, .mil, .mk, .ml, .mm, .mobi, .ms, .mt, .mu, .museum, .mv, .mw, .my, .mz, .name, .nf, .ni, .nl, .no, .np, .nu, .nz, .om, .pa, .pe, .pf, .pg, .pl, .pn, .pr, .pro, .pw, .py, .root, .rs, .ru, .rw, .sb, .sc, .sd, .se, .sj, .sn, .su, .sy, .tc, .td, .tel, .tg, .th, .tj, .tk, .tl, .tm, .tp, .tr, .travel, .tt, .tv, .tz, .ua, .uk, .um, .uz, .va, .vc, .ve, .vg, .vi, .vu, .ye, .yu, .za, .zm, .zw
EDIT: Clearly, this approach is not definitive. I tried to register two letter domains at several of these and was unsuccessful (e.g., domai.nr might say the domain is available, but the registrar they link to says it is invalid). YMMV.