[Droid Incredible Q&A, Help & Troubleshooting] rdmerck:
busybox doesn't affect your ability to apply an OTA, it adds functionality to your su permissions by implementing other command line features of Linux.

Your phone is harnessing a neutered down version of Linux. Not all commands are available to be used. This is mainly because the average Android user doesn't need it, and the storage space that is needed to supplement these commands/programs doesn't warrant having them installed. This is especially true when you consider the average Android user isn't going to have root access, and have a need to use these commands from a command prompt and/or root-access enabled application.

Since rooting is giving you superuser permission, it would only make sense to enhance your superuser abilities by having the right tools at your disposal. Busybox implements this by suppling a shi*load of binaries (executables) available to you at a minimum amount of storage space.

Having busybox installed gives you the ability to implement:

[, [[, acpid, addgroup, adduser, adjtimex, ar, arp, arping, ash,

awk, basename, beep, blkid, brctl, bunzip2, bzcat, bzip2, cal, cat,

catv, chat, chattr, chgrp, chmod, chown, chpasswd, chpst, chroot,

chrt, chvt, cksum, clear, cmp, comm, cp, cpio, crond, crontab,

cryptpw, cut, date, dc, dd, deallocvt, delgroup, deluser, depmod,

devmem, df, dhcprelay, diff, dirname, dmesg, dnsd, dnsdomainname,

dos2unix, dpkg, du, dumpkmap, dumpleases, echo, ed, egrep, eject,

env, envdir, envuidgid, expand, expr, fakeidentd, false, fbset,

fbsplash, fdflush, fdformat, fdisk, fgrep, find, findfs, flash_lock,

flash_unlock, fold, free, freeramdisk, fsck, fsck.minix, fsync,

ftpd, ftpget, ftpput, fuser, getopt, getty, grep, gunzip, gzip, hd,

hdparm, head, hexdump, hostid, hostname, httpd, hush, hwclock, id,

ifconfig, ifdown, ifenslave, ifplugd, ifup, inetd, init, inotifyd,

insmod, install, ionice, ip, ipaddr, ipcalc, ipcrm, ipcs, iplink,

iproute, iprule, iptunnel, kbd_mode, kill, killall, killall5, klogd,

last, length, less, linux32, linux64, linuxrc, ln, loadfont,

loadkmap, logger, login, logname, logread, losetup, lpd, lpq, lpr,

ls, lsattr, lsmod, lzmacat, lzop, lzopcat, makemime, man, md5sum,

mdev, mesg, microcom, mkdir, mkdosfs, mkfifo, mkfs.minix, mkfs.vfat,

mknod, mkpasswd, mkswap, mktemp, modprobe, more, mount, mountpoint,

mt, mv, nameif, nc, netstat, nice, nmeter, nohup, nslookup, od,

openvt, passwd, patch, pgrep, pidof, ping, ping6, pipe_progress,

pivot_root, pkill, popmaildir, printenv, printf, ps, pscan, pwd,

raidautorun, rdate, rdev, readlink, readprofile, realpath,

reformime, renice, reset, resize, rm, rmdir, rmmod, route, rpm,

rpm2cpio, rtcwake, run-parts, runlevel, runsv, runsvdir, rx, script,

scriptreplay, sed, sendmail, seq, setarch, setconsole, setfont,

setkeycodes, setlogcons, setsid, setuidgid, sh, sha1sum, sha256sum,

sha512sum, showkey, slattach, sleep, softlimit, sort, split,

start-stop-daemon, stat, strings, stty, su, sulogin, sum, sv,

svlogd, swapoff, swapon, switch_root, sync, sysctl, syslogd, tac,

tail, tar, taskset, tcpsvd, tee, telnet, telnetd, test, tftp, tftpd,

time, timeout, top, touch, tr, traceroute, true, tty, ttysize,

udhcpc, udhcpd, udpsvd, umount, uname, uncompress, unexpand, uniq,

unix2dos, unlzma, unlzop, unzip, uptime, usleep, uudecode, uuencode,

vconfig, vi, vlock, volname, watch, watchdog, wc, wget, which, who,

whoami, xargs, yes, zcat, zcip